Question 1

Find the equation of the circle
$$x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$$
that passes through the points $( 1,9 ) , ( - 4,4 ) , ( 6,4 )$.

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - x - 4 y - 8 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y + 42 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 25 = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - x - 4 y - 25 = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - x - 4 y - 8 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y + 42 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 25 = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - x - 4 y - 25 = 0$ A

Question 2

Solve the system of linear equations
$\left\{ \begin{array} { l } 4 x _ { 1 } - 8 x _ { 2 } - 4 x _ { 3 } - 8 x _ { 4 } = 0 \ 12 x _ { 1 } - 20 x _ { 2 } - 8 x _ { 3 } - 12 x _ { 4 } = - 9 \ 8 x _ { 1 } - 20 x _ { 2 } - 8 x _ { 3 } - 20 x _ { 4 } = 6 \ - 4 x _ { 1 } + 16 x _ { 2 } + 16 x _ { 3 } + 44 x _ { 4 } = 0 \end{array} \mid \left[ \begin{array} { c c c c } - 24 & 7 & 1 & - 2 \ - 10 & 3 & 0 & - 1 \ - 29 & 7 & 3 & - 2 \ 12 & - 3 & - 1 & 1 \end{array} \right] . \right.$

Accepted Answer

A) 
$\left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 57 } { 4 } \ - \frac { 27 } { 4 } \ - \frac { 45 } { 4 } \ \frac { 21 } { 4 } \end{array} \right]$ 
B) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 21 } { 4 } \
- \frac { 15 } { 4 } \
\frac { 27 } { 4 } \
- \frac { 27 } { 4 }
\end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 27 } { 4 } \
- \frac { 57 } { 4 } \
0 \
\frac { 21 } { 4 }
\end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 9 } { 4 } \
\frac { 3 } { 4 } \
0 \
\frac { 3 } { 2 }
\end{array} \right]$ 
E) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
0 \
- \frac { 3 } { 4 } \
0 \
- \frac { 3 } { 2 }
\end{array} \right]$ 
A) 
$\left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 57 } { 4 } \ - \frac { 27 } { 4 } \ - \frac { 45 } { 4 } \ \frac { 21 } { 4 } \end{array} \right]$ 
B) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 21 } { 4 } \
- \frac { 15 } { 4 } \
\frac { 27 } { 4 } \
- \frac { 27 } { 4 }
\end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 27 } { 4 } \
- \frac { 57 } { 4 } \
0 \
\frac { 21 } { 4 }
\end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 9 } { 4 } \
\frac { 3 } { 4 } \
0 \
\frac { 3 } { 2 }
\end{array} \right]$ 
E) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
0 \
- \frac { 3 } { 4 } \
0 \
- \frac { 3 } { 2 }
\end{array} \right]$ A

Question 3

Find $| A B |$, if
$A = \left[ \begin{array} { r r r } 5 & - 2 & - 2 \ - 3 & 4 & - 1 \ - 5 & 6 & 2 \end{array} \right] , B = \left[ \begin{array} { r r r } 1 & - 1 & - 3 \ - 5 & - 3 & 4 \ - 5 & - 1 & - 2 \end{array} \right]$

Accepted Answer

A)  3080 
B)  616 
C)  150 
D)  280 
E)  1300 
A)  3080 
B)  616 
C)  150 
D)  280 
E)  1300 A

Question 4

Solve system of equations by the method of substitution.
$$\left\{ \begin{array} { r } 
15 x ^ { 3 } - 25 y = 0 \
15 x - y = 0
\end{array} \right.$$

Accepted Answer

A)  $( 0,0 ) , ( - 5 , - 75 ) , ( 5,75 )$ 
B)  $( 0,0 ) , ( - 5,75 ) , ( 5,75 )$ 
C)  $( 0,0 ) , ( 5 , - 75 ) , ( 5,75 )$ 
D)  $( 0,0 ) , ( - 5,76 ) , ( 5,76 )$ 
E)  $( 0,0 ) , ( - 5 , - 74 ) , ( 5,74 )$ 
A)  $( 0,0 ) , ( - 5 , - 75 ) , ( 5,75 )$ 
B)  $( 0,0 ) , ( - 5,75 ) , ( 5,75 )$ 
C)  $( 0,0 ) , ( 5 , - 75 ) , ( 5,75 )$ 
D)  $( 0,0 ) , ( - 5,76 ) , ( 5,76 )$ 
E)  $( 0,0 ) , ( - 5 , - 74 ) , ( 5,74 )$

Question 5

Given: $A = \left[ \begin{array} { r r r } - 6 & - 10 & 7 \ - 2 & 4 & 3 \end{array} \right] , B = \left[ \begin{array} { r r r } - 1 & 7 & - 3 \ 1 & 2 & - 2 \end{array} \right] , c = - 4$ and $d = 2$ determine $c A + d B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } 22 & - 3 & 4 \ 10 & 6 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 26 & 26 & - 22 \ 6 & - 20 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 22 & 54 & - 34 \ 10 & - 12 & - 16 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 22 & 54 & - 34 \ - 1 & 6 & 1 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { r r r } 22 & - 3 & 4 \ 10 & 6 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 26 & 26 & - 22 \ 6 & - 20 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 22 & 54 & - 34 \ 10 & - 12 & - 16 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 22 & 54 & - 34 \ - 1 & 6 & 1 \end{array} \right]$ 
E)  not possible

Question 6

If possible, find $3 A + 4 B$.
$$A = \left[ \begin{array} { c c c } 
- 4 & 3 & 9 \
3 & - 2 & 5
\end{array} \right] , B = \left[ \begin{array} { c c c } 
- 8 & 9 & 5 \
0 & 2 & 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c c } 20 & - 27 & 7 \ 9 & - 14 & 11 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } - 12 & 12 & 14 \ 3 & 0 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 44 & 45 & 47 \ 9 & 2 & 19 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { c c c } 20 & - 27 & 7 \ 9 & - 14 & 11 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } - 12 & 12 & 14 \ 3 & 0 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 44 & 45 & 47 \ 9 & 2 & 19 \end{array} \right]$ 
E)  not possible

Question 7

Solve the system of linear equations
$$\left\{ \begin{array} { l } 
6 x _ { 1 } - 12 x _ { 2 } - 6 x _ { 3 } - 12 x _ { 4 } = 0 \
18 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 18 x _ { 4 } = - 3 \
12 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 30 x _ { 4 } = 2 \
- 6 x _ { 1 } + 24 x _ { 2 } + 24 x _ { 3 } + 66 x _ { 4 } = 0 \
{ \left[ \begin{array} { c c c c } 
- 24 & 7 & 1 & - 2 \
- 10 & 3 & 0 & - 1 \
- 29 & 7 & 3 & - 2 \
12 & - 3 & - 1 & 1
\end{array} \right] }
\end{array} \right.$$

Accepted Answer

A) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 19 } { 6 } \
- \frac { 3 } { 2 } \
- \frac { 5 } { 2 } \
\frac { 7 } { 6 }
\end{array} \right]$ 
B) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 7 } { 6 } \
- \frac { 5 } { 6 } \
\frac { 3 } { 2 } \
- \frac { 3 } { 2 }
\end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 3 } { 2 } \
- \frac { 19 } { 6 } \
0 \
\frac { 7 } { 6 }
\end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 1 } { 2 } \
\frac { 1 } { 6 } \
0 \
\frac { 1 } { 3 }
\end{array} \right]$ 
E) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
0 \
- \frac { 1 } { 6 } \
0 \
- \frac { 1 } { 3 }
\end{array} \right]$ 
A) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 19 } { 6 } \
- \frac { 3 } { 2 } \
- \frac { 5 } { 2 } \
\frac { 7 } { 6 }
\end{array} \right]$ 
B) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 7 } { 6 } \
- \frac { 5 } { 6 } \
\frac { 3 } { 2 } \
- \frac { 3 } { 2 }
\end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 3 } { 2 } \
- \frac { 19 } { 6 } \
0 \
\frac { 7 } { 6 }
\end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 1 } { 2 } \
\frac { 1 } { 6 } \
0 \
\frac { 1 } { 3 }
\end{array} \right]$ 
E) 
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
0 \
- \frac { 1 } { 6 } \
0 \
- \frac { 1 } { 3 }
\end{array} \right]$

Question 8

Solve for $X$ in the equation given.
$$9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 
6 & - 5 & 3 \
8 & - 3 & - 7
\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } 
3 & 5 & - 1 \
1 & - 2 & 5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c c } 72 & - 15 & 21 \ 78 & - 39 & - 33 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 9 & 0 & 2 \ 9 & - 5 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 24 & - 5 & 7 \ 26 & - 13 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 12 & - 25 & 11 \ 22 & - 5 & - 31 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { c c c } 72 & - 15 & 21 \ 78 & - 39 & - 33 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 9 & 0 & 2 \ 9 & - 5 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 24 & - 5 & 7 \ 26 & - 13 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 12 & - 25 & 11 \ 22 & - 5 & - 31 \end{array} \right]$ 
E)  not possible

Question 9

Given:
$A = \left[ \begin{array} { r r r } 8 & - 7 & 0 \ - 5 & - 2 & 3 \end{array} \right] , B = \left[ \begin{array} { r r r } 3 & 0 & 7 \ 4 & 9 & - 2 \end{array} \right] , c = 8$ and $d = - 3$ determine $c A + d B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } 55 & - 7 & 7 \ - 52 & 7 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 73 & - 56 & 21 \ - 28 & 11 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 52 & - 43 & 30 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 1 & 7 & 1 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { r r r } 55 & - 7 & 7 \ - 52 & 7 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 73 & - 56 & 21 \ - 28 & 11 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 52 & - 43 & 30 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 1 & 7 & 1 \end{array} \right]$ 
E)  not possible

Question 10

Solve using any method.
$$\left\{ \begin{aligned}
- 7 x - 9 y & = - 6 \
y & = x - 3
\end{aligned} \right.$$

Accepted Answer

A)  $( 2 , - 1 )$ 
B)  $\left( 1 , - \frac { 3 } { 7 } \right)$ 
C)  $\left( - \frac { 21 } { 16 } , - \frac { 27 } { 16 } \right)$ 
D)  $\left( \frac { 33 } { 16 } , - \frac { 15 } { 16 } \right)$ 
E)  inconsistent 
A)  $( 2 , - 1 )$ 
B)  $\left( 1 , - \frac { 3 } { 7 } \right)$ 
C)  $\left( - \frac { 21 } { 16 } , - \frac { 27 } { 16 } \right)$ 
D)  $\left( \frac { 33 } { 16 } , - \frac { 15 } { 16 } \right)$ 
E)  inconsistent

Question 11

Solve the system by the method of elimination. Round numbers to three decimal places.
$$\left\{ \begin{array} { c } 
5.2 x + 8.1 y = 6.9 \
- 2.6 x + 1.1 y = - 0.7
\end{array} \right.$$

Accepted Answer

A)  $( 2.020,1.873 )$ 
B)  $( 0.495,0.534 )$ 
C)  $( - 0.864,1.407 )$ 
D)  $( 0.192,0.728 )$ 
E)  no solution 
A)  $( 2.020,1.873 )$ 
B)  $( 0.495,0.534 )$ 
C)  $( - 0.864,1.407 )$ 
D)  $( 0.192,0.728 )$ 
E)  no solution

Question 12

Determine which ordered pair is a solution of the system.
$$\left\{ \begin{aligned}
x - 2 y ^ { 2 } & = - 7 \
- 5 x + 6 y & = 7
\end{aligned} \right.$$

Accepted Answer

A)  $( 1,2 )$ 
B)  $( 1 , - 2 )$ 
C)  $( - 1,2 )$ 
D)  $( - 1 , - 2 )$ 
E)  $( 0 , - 2 )$ 
A)  $( 1,2 )$ 
B)  $( 1 , - 2 )$ 
C)  $( - 1,2 )$ 
D)  $( - 1 , - 2 )$ 
E)  $( 0 , - 2 )$

Question 13

Solve for $x$ given the following equation involving a determinant.
$$\left| \begin{array} { c c } 
x + 2 & 5 \
- 1 & x + 8
\end{array} \right| = 0$$

Accepted Answer

A)  $x = 7,3$ 
B)  $x = - 8 , - 2$ 
C)  $x = 8,2$ 
D)  $x = - 7 , - 3$ 
E)  $x = 6 , - 5$ 
A)  $x = 7,3$ 
B)  $x = - 8 , - 2$ 
C)  $x = 8,2$ 
D)  $x = - 7 , - 3$ 
E)  $x = 6 , - 5$

Question 14

Solve the system of linear equations.
$$\left\{ \begin{array} { c } 
x + y + z + w = 3 \
- x - y + z + w = - 5 \
x \quad + 3 z + w = - 6 \
- 4 x - 4 y - 2 z - w = - 13
\end{array} \right.$$

Accepted Answer

A)  $( - 1,5,1 , - 2 )$ 
B)  $( - 1 , - 2,5,1 )$ 
C)  $( 1,5 , - 2 , - 1 )$ 
D)  $( - 1,5 , - 2,1 )$ 
E)  inconsistent 
A)  $( - 1,5,1 , - 2 )$ 
B)  $( - 1 , - 2,5,1 )$ 
C)  $( 1,5 , - 2 , - 1 )$ 
D)  $( - 1,5 , - 2,1 )$ 
E)  inconsistent

Question 15

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables $x , y$, and $z$.)
$\left[ \begin{array} { c c c : c } 1 & 4 & - 3 & - 23 \ 0 & 1 & 4 & 19 \ 0 & 0 & 1 & 5 \end{array} \right]$

Accepted Answer

A)  $x = - 44 , y = 3 , z = - 3$ 
B)  $x = - 1 , y = - 4 , z = 5$ 
C)  $x = - 4 , y = 1 , z = - 5$ 
D)  $x = - 4 , y = - 1 , z = 5$ 
E)  $x = 1 , y = 5 , z = 4$ 
A)  $x = - 44 , y = 3 , z = - 3$ 
B)  $x = - 1 , y = - 4 , z = 5$ 
C)  $x = - 4 , y = 1 , z = - 5$ 
D)  $x = - 4 , y = - 1 , z = 5$ 
E)  $x = 1 , y = 5 , z = 4$

Question 16

Determine the order of the matrix.
$$\left[ \begin{array} { c c c } 
- 4 & - 8 & 2 \
0 & - 7 & - 4
\end{array} \right]$$

Accepted Answer

A)  $2 \times 3$ 
B)  $3 \times 3$ 
C)  $3 \times 1$ 
D)  $3 \times 2$ 
E)  $2 \times 2$ 
A)  $2 \times 3$ 
B)  $3 \times 3$ 
C)  $3 \times 1$ 
D)  $3 \times 2$ 
E)  $2 \times 2$

Question 17

Evaluate the expression.
$$\left[ \begin{array} { c } 
- 5 \
- 1 \
5
\end{array} \right] \left( \left[ \begin{array} { l l } 
9 & - 7
\end{array} \right] + \left[ \begin{array} { l l } 
- 7 & - 8
\end{array} \right] \right)$$

Accepted Answer

A) 
$\left[ \begin{array} { c } - 10 \ - 2 \ 10 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - 10 & 75 \ - 2 & 15 \ 10 & - 75 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 10 & - 2 & 10 \ 75 & 15 & - 75 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c c } - 45 & 35 & 35 & 40 \ - 9 & 7 & 7 & 8 \ 45 & - 35 & - 35 & - 40 \end{array} \right]$ 
E)  not possible 
A) 
$\left[ \begin{array} { c } - 10 \ - 2 \ 10 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - 10 & 75 \ - 2 & 15 \ 10 & - 75 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 10 & - 2 & 10 \ 75 & 15 & - 75 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c c } - 45 & 35 & 35 & 40 \ - 9 & 7 & 7 & 8 \ 45 & - 35 & - 35 & - 40 \end{array} \right]$ 
E)  not possible

Question 18

Match the system of linear equations with its graph.
$$\left\{ \begin{array} { r } 
3 x + 6 y - 12 = 0 \
15 x - 5 y - 10 = 0
\end{array} \right.$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

E) 
  
A) 
  
B) 
  
C) 
  
D)

E)

Question 19

Write the system of linear equations represented by the augmented matrix. (Use variables $x , y , z$, and $w$.)
$\left[ \begin{array} { c c c c : c } - 4 & 0 & 0 & - 9 & - 9 \ 7 & - 8 & 0 & 0 & 1 \ 0 & - 4 & - 7 & - 9 & - 8 \ 0 & 0 & - 4 & 1 & - 8 \end{array} \right]$

Accepted Answer

A) 
$\left\{ \begin{aligned} - 4 x - 9 y & = - 9 \ 7 x - 8 y & = 1 \ - 4 x - 7 y - 9 z & = - 8 \ - 4 x + y & = - 8 \end{aligned} \right.$ 
B) 
$\left\{ \begin{aligned} - 4 x - 9 z & = - 9 \ 7 x - 8 y & = 1 \ - 4 y - - 7 z - 9 w & = - 8 \ - 4 z + w & = - 8 \end{aligned} \right.$ 
C) 
$\left\{ \begin{array} { r l r } - 4 x & - 9 z & = - 9 \ 7 x & - 8 z & = 1 \ - 4 y - 7 z - 9 w & = - 8 \ - 4 z + w & = - 8 \end{array} \right.$ 
D) 
$\left\{\begin{array}{lr}
-4 x&  -9 w=-9\
7 x-8 y & \quad=1\
 \quad -4 y-7 z & -9 w=-8\
 \quad -4 y+z & \quad=-8
\end{array}\right.$ 
E) 
$\left\{\begin{array}{lr}
-4 x&  -9 w=-9\
7 x-8 y & \quad=1\
 \quad -4 y-7 z & -9 w=-8\
 \quad -4 y+z & =-8
\end{array}\right.$ 
A) 
$\left\{ \begin{aligned} - 4 x - 9 y & = - 9 \ 7 x - 8 y & = 1 \ - 4 x - 7 y - 9 z & = - 8 \ - 4 x + y & = - 8 \end{aligned} \right.$ 
B) 
$\left\{ \begin{aligned} - 4 x - 9 z & = - 9 \ 7 x - 8 y & = 1 \ - 4 y - - 7 z - 9 w & = - 8 \ - 4 z + w & = - 8 \end{aligned} \right.$ 
C) 
$\left\{ \begin{array} { r l r } - 4 x & - 9 z & = - 9 \ 7 x & - 8 z & = 1 \ - 4 y - 7 z - 9 w & = - 8 \ - 4 z + w & = - 8 \end{array} \right.$ 
D) 
$\left\{\begin{array}{lr}
-4 x&  -9 w=-9\
7 x-8 y & \quad=1\
 \quad -4 y-7 z & -9 w=-8\
 \quad -4 y+z & \quad=-8
\end{array}\right.$ 
E) 
$\left\{\begin{array}{lr}
-4 x&  -9 w=-9\
7 x-8 y & \quad=1\
 \quad -4 y-7 z & -9 w=-8\
 \quad -4 y+z & =-8
\end{array}\right.$

Question 20

Solve for $X$ in the equation given.
$$16 A + 12 B = - 4 X , A = \left[ \begin{array} { c c c } 
5 & 6 & 3 \
- 2 & 5 & - 4
\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } 
- 5 & 8 & - 1 \
- 3 & - 9 & - 5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c c } 20 & 192 & 36 \ - 68 & - 28 & - 124 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 0 & 14 & 2 \ - 5 & - 4 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 5 & - 48 & - 9 \ 17 & 7 & 31 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 35 & 0 & - 15 \ - 1 & - 47 & 1 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { c c c } 20 & 192 & 36 \ - 68 & - 28 & - 124 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 0 & 14 & 2 \ - 5 & - 4 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 5 & - 48 & - 9 \ 17 & 7 & 31 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 35 & 0 & - 15 \ - 1 & - 47 & 1 \end{array} \right]$ 
E)  not possible

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( 1,9 ) , ( - 4,4 ) , ( 6,4 )$ .

Find $| A B |$ , if $A = \left[ \begin{array} { r r r } 5 & - 2 & - 2 \\ - 3 & 4 & - 1 \\ - 5 & 6 & 2 \end{array} \right] , B = \left[ \begin{array} { r r r } 1 & - 1 & - 3 \\ - 5 & - 3 & 4 \\ - 5 & - 1 & - 2 \end{array} \right]$

Solve system of equations by the method of substitution. $\left\{ \begin{array} { r } 15 x ^ { 3 } - 25 y = 0 \\15 x - y = 0\end{array} \right.$

Given: $A = \left[ \begin{array} { r r r } - 6 & - 10 & 7 \\ - 2 & 4 & 3 \end{array} \right] , B = \left[ \begin{array} { r r r } - 1 & 7 & - 3 \\ 1 & 2 & - 2 \end{array} \right] , c = - 4$ and $d = 2$ determine $c A + d B$ .

If possible, find $3 A + 4 B$ . $A = \left[ \begin{array} { c c c } - 4 & 3 & 9 \\3 & - 2 & 5\end{array} \right] , B = \left[ \begin{array} { c c c } - 8 & 9 & 5 \\0 & 2 & 1\end{array} \right]$

Solve for $X$ in the equation given. $9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 6 & - 5 & 3 \\8 & - 3 & - 7\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } 3 & 5 & - 1 \\1 & - 2 & 5\end{array} \right]$

Given: $A = \left[ \begin{array} { r r r } 8 & - 7 & 0 \\ - 5 & - 2 & 3 \end{array} \right] , B = \left[ \begin{array} { r r r } 3 & 0 & 7 \\ 4 & 9 & - 2 \end{array} \right] , c = 8$ and $d = - 3$ determine $c A + d B$ .

Solve using any method. $\left\{ \begin{aligned}- 7 x - 9 y & = - 6 \\y & = x - 3\end{aligned} \right.$

Solve the system by the method of elimination. Round numbers to three decimal places. $\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.$

Determine which ordered pair is a solution of the system. $\left\{ \begin{aligned}x - 2 y ^ { 2 } & = - 7 \\- 5 x + 6 y & = 7\end{aligned} \right.$

Solve for $x$ given the following equation involving a determinant. $\left| \begin{array} { c c } x + 2 & 5 \\- 1 & x + 8\end{array} \right| = 0$

Solve the system of linear equations. $\left\{ \begin{array} { c } x + y + z + w = 3 \\- x - y + z + w = - 5 \\x \quad + 3 z + w = - 6 \\- 4 x - 4 y - 2 z - w = - 13\end{array} \right.$

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables $x , y$ , and $z$ .) $\left[ \begin{array} { c c c : c } 1 & 4 & - 3 & - 23 \\ 0 & 1 & 4 & 19 \\ 0 & 0 & 1 & 5 \end{array} \right]$

Determine the order of the matrix. $\left[ \begin{array} { c c c } - 4 & - 8 & 2 \\0 & - 7 & - 4\end{array} \right]$

Evaluate the expression. $\left[ \begin{array} { c } - 5 \\- 1 \\5\end{array} \right] \left( \left[ \begin{array} { l l } 9 & - 7\end{array} \right] + \left[ \begin{array} { l l } - 7 & - 8\end{array} \right] \right)$

Match the system of linear equations with its graph. $\left\{ \begin{array} { r } 3 x + 6 y - 12 = 0 \\15 x - 5 y - 10 = 0\end{array} \right.$

Write the system of linear equations represented by the augmented matrix. (Use variables $x , y , z$ , and $w$ .) $\left[ \begin{array} { c c c c : c } - 4 & 0 & 0 & - 9 & - 9 \\ 7 & - 8 & 0 & 0 & 1 \\ 0 & - 4 & - 7 & - 9 & - 8 \\ 0 & 0 & - 4 & 1 & - 8 \end{array} \right]$

Solve for $X$ in the equation given. $16 A + 12 B = - 4 X , A = \left[ \begin{array} { c c c } 5 & 6 & 3 \\- 2 & 5 & - 4\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } - 5 & 8 & - 1 \\- 3 & - 9 & - 5\end{array} \right]$

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Exam 7: Linear Systems and Matrices

Find the equation of the circle x2+y2+Dx+Ey+F=0x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0x2+y2+Dx+Ey+F=0 that passes through the points (1,9),(−4,4),(6,4)( 1,9 ) , ( - 4,4 ) , ( 6,4 )(1,9),(−4,4),(6,4) .

Solve system of equations by the method of substitution. {15x3−25y=015x−y=0\left\{ \begin{array} { r } 15 x ^ { 3 } - 25 y = 0 \\15 x - y = 0\end{array} \right.{15x3−25y=015x−y=0​

If possible, find 3A+4B3 A + 4 B3A+4B . A=[−4393−25],B=[−895021]A = \left[ \begin{array} { c c c } - 4 & 3 & 9 \\3 & - 2 & 5\end{array} \right] , B = \left[ \begin{array} { c c c } - 8 & 9 & 5 \\0 & 2 & 1\end{array} \right]A=[−43​3−2​95​],B=[−80​92​51​]

Solve using any method. {−7x−9y=−6y=x−3\left\{ \begin{aligned}- 7 x - 9 y & = - 6 \\y & = x - 3\end{aligned} \right.{−7x−9yy​=−6=x−3​

Solve the system by the method of elimination. Round numbers to three decimal places. {5.2x+8.1y=6.9−2.6x+1.1y=−0.7\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.{5.2x+8.1y=6.9−2.6x+1.1y=−0.7​

Determine which ordered pair is a solution of the system. {x−2y2=−7−5x+6y=7\left\{ \begin{aligned}x - 2 y ^ { 2 } & = - 7 \\- 5 x + 6 y & = 7\end{aligned} \right.{x−2y2−5x+6y​=−7=7​

Solve for xxx given the following equation involving a determinant. ∣x+25−1x+8∣=0\left| \begin{array} { c c } x + 2 & 5 \\- 1 & x + 8\end{array} \right| = 0​x+2−1​5x+8​​=0

Determine the order of the matrix. [−4−820−7−4]\left[ \begin{array} { c c c } - 4 & - 8 & 2 \\0 & - 7 & - 4\end{array} \right][−40​−8−7​2−4​]

Evaluate the expression. [−5−15]([9−7]+[−7−8])\left[ \begin{array} { c } - 5 \\- 1 \\5\end{array} \right] \left( \left[ \begin{array} { l l } 9 & - 7\end{array} \right] + \left[ \begin{array} { l l } - 7 & - 8\end{array} \right] \right)​−5−15​​([9​−7​]+[−7​−8​])

Match the system of linear equations with its graph. {3x+6y−12=015x−5y−10=0\left\{ \begin{array} { r } 3 x + 6 y - 12 = 0 \\15 x - 5 y - 10 = 0\end{array} \right.{3x+6y−12=015x−5y−10=0​