Question 1

Determine which inequality matches the graph.
-

Accepted Answer

A)  $y  - x ^ { 2 } - 2$ 
C)  $y > x ^ { 2 } + 2$ 
D)  $y > x ^ { 2 } - 2$ 
A)  $y  - x ^ { 2 } - 2$ 
C)  $y > x ^ { 2 } + 2$ 
D)  $y > x ^ { 2 } - 2$

Question 2

Perform the indicated operation, if possible.
-$$\left[ \begin{array} { r r } 
- 1 & 0 \
5 & 2
\end{array} \right] - \left[ \begin{array} { r r } 
- 1 & 5 \
3 & 1
\end{array} \right]$$

Accepted Answer

A) 
$[ - 2 ]$ 
B) 
$\left[ \begin{array} { r r } 0 & - 5 \ 2 & 1 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 0 & 5 \ - 2 & - 1 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 2 & 5 \ 8 & 3 \end{array} \right]$ 
A) 
$[ - 2 ]$ 
B) 
$\left[ \begin{array} { r r } 0 & - 5 \ 2 & 1 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 0 & 5 \ - 2 & - 1 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 2 & 5 \ 8 & 3 \end{array} \right]$

Question 3

Find the partial fraction decomposition.
-$$\frac { 5 x - 2 } { x ^ { 3 } - 4 x } = \frac { A } { x } + \frac { B } { x + 2 } + \frac { C } { x - 2 }$$

Accepted Answer

A)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 } , \mathrm { C } = 1$ 
B)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = 1 , \mathrm { C } = \frac { 3 } { 2 }$ 
C)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = 1 , \mathrm { C } = - \frac { 3 } { 2 }$ 
D)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = - \frac { 3 } { 2 } , \mathrm { C } = 1$ 
A)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 } , \mathrm { C } = 1$ 
B)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = 1 , \mathrm { C } = \frac { 3 } { 2 }$ 
C)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = 1 , \mathrm { C } = - \frac { 3 } { 2 }$ 
D)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = - \frac { 3 } { 2 } , \mathrm { C } = 1$

Question 4

Write the system of equations associated with the augmented matrix. Do not solve.
-$\left[ \begin{array} { r r r r } - 8 & - 4 & - 7 & - 6 \ 4 & 3 & 0 & 6 \ 8 & 0 & 8 & 2 \end{array} \right]$

Accepted Answer

A)  $- 8 x - 4 y - 7 z = - 6$
$4 x + \quad 3 z = 6$
$8 x + 8 y = 2$ 
B)  $- 8 x - 4 y - 7 z = - 6$
$4 x + 3 y + 6 z = 0$
$8 x + 8 y + 2 z = 0$ 
C)  $- 8 x - 4 y - 7 z = - 6$
$4 x + 3 y = 6$
$8 x + 8 y = 2$ 
D)  $- 8 x - 4 y - 7 z = - 6$
$4 x + 3 y = 6$
$8 x + 8 z = 2$ 
A)  $- 8 x - 4 y - 7 z = - 6$
$4 x + \quad 3 z = 6$
$8 x + 8 y = 2$ 
B)  $- 8 x - 4 y - 7 z = - 6$
$4 x + 3 y + 6 z = 0$
$8 x + 8 y + 2 z = 0$ 
C)  $- 8 x - 4 y - 7 z = - 6$
$4 x + 3 y = 6$
$8 x + 8 y = 2$ 
D)  $- 8 x - 4 y - 7 z = - 6$
$4 x + 3 y = 6$
$8 x + 8 z = 2$

Question 5

Write the system of equations associated with the augmented matrix. Do not solve.
-$$\left[ \begin{array} { r r r } 
- 9 & - 3 & - 9 \
9 & - 6 & - 6
\end{array} \right]$$

Accepted Answer

A)  $- 9 x - 3 y = - 9$
$9 x - 6 y = - 6$ 
B)  $- 9 x - 3 y = - 9$
$- 6 x + 9 y = - 6$ 
C)  $- 9 x - 3 y = 9$
$9 x - 6 y = 6$ 
D)  $- 3 x - 9 y = - 9$
$9 x - 6 y = - 6$ 
A)  $- 9 x - 3 y = - 9$
$9 x - 6 y = - 6$ 
B)  $- 9 x - 3 y = - 9$
$- 6 x + 9 y = - 6$ 
C)  $- 9 x - 3 y = 9$
$9 x - 6 y = 6$ 
D)  $- 3 x - 9 y = - 9$
$9 x - 6 y = - 6$

Question 6

Use the graph to estimate any solutions of the system.
-$\begin{array}{l}
y=-2+x-x^{2} \
y=-3+x
\end{array}$
 
$[ - 5,5 ]$ by $[ - 5,5 ]$

Accepted Answer

A)  $( 1 , - 2 )$ 
B)  $( 1 , - 2 )$ and $( - 1 , - 4 )$ 
C)  $( 1 , - 2 )$ and $( 0 , - 4 )$ 
D)  $( 0.5 , - 2 )$ and $( - 1 , - 4 )$ 
A)  $( 1 , - 2 )$ 
B)  $( 1 , - 2 )$ and $( - 1 , - 4 )$ 
C)  $( 1 , - 2 )$ and $( 0 , - 4 )$ 
D)  $( 0.5 , - 2 )$ and $( - 1 , - 4 )$

Question 7

Determine the order of the matrix.
-$$\left[ \begin{array} { r r } 
4 & 8 \
- 5 & - 1
\end{array} \right]$$

Accepted Answer

A)  4 
B)  1 
C)  2 
D)  $2 \times 2$ 
A)  4 
B)  1 
C)  2 
D)  $2 \times 2$

Question 8

Find the determinant of the given matrix.
-$$\left[ \begin{array} { l l l l } 
0 & 0 & 0 & 7 \
9 & 8 & 8 & 4 \
7 & 7 & 4 & 8 \
1 & 4 & 7 & 2
\end{array} \right]$$

Accepted Answer

A)  $- 28$ 
B)  $- 49$ 
C)  735 
D)  $- 735$ 
A)  $- 28$ 
B)  $- 49$ 
C)  735 
D)  $- 735$

Question 9

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix.
-

Accepted Answer

The answer of Determine which elementary row operation(s) applied to...

Question 10

Find the matrix product, if possible.
-$\left[ \begin{array} { r r r } 5 & 1 & - 8 \ - 2 & - 8 & 5 \ - 4 & 2 & 4 \end{array} \right] \left[ \begin{array} { r r r } 5 & 8 & - 6 \ - 5 & 6 & - 6 \ 3 & 8 & - 9 \end{array} \right]$

Accepted Answer

A) 
$\left[ \begin{array} { r r r } - 4 & 45 & - 18 \ - 18 & - 24 & 12 \ 36 & 15 & - 24 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r r } - 4 & - 18 & 36 \ 45 & - 24 & 15 \ - 18 & 12 & - 24 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r r } 25 & 8 & 48 \ 10 & - 48 & - 30 \ - 12 & 16 & - 36 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r r } 5 & 1 & - 8 \ - 2 & - 8 & 5 \ - 4 & 2 & 4 \ 5 & 8 & - 6 \ - 5 & 6 & - 6 \ 3 & 8 & - 9 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r r r } - 4 & 45 & - 18 \ - 18 & - 24 & 12 \ 36 & 15 & - 24 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r r } - 4 & - 18 & 36 \ 45 & - 24 & 15 \ - 18 & 12 & - 24 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r r } 25 & 8 & 48 \ 10 & - 48 & - 30 \ - 12 & 16 & - 36 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r r } 5 & 1 & - 8 \ - 2 & - 8 & 5 \ - 4 & 2 & 4 \ 5 & 8 & - 6 \ - 5 & 6 & - 6 \ 3 & 8 & - 9 \end{array} \right]$

Question 11

Identify the element specified for the matrix.
-$$\left[ \begin{array} { r r r r r } 
- 6 & 1 & - 5 & 8 & 3 \
- 9 & - 8 & - 5 & - 7 & 3 \
5 & 0 & - 1 & - 2 & 3 \
- 3 & 5 & - 9 & 1 & 6
\end{array} \right]$$
a11

Accepted Answer

A)  $- 6$ 
B)  3 
C)  5 
D)  $- 8$ 
A)  $- 6$ 
B)  3 
C)  5 
D)  $- 8$

Question 12

Find the matrix product, if possible.
-$$\left[ \begin{array} { r r } 
- 1 & 3 \
3 & 6
\end{array} \right] \left[ \begin{array} { l l l } 
0 & - 2 & 4 \
1 & - 3 & 2
\end{array} \right]$$

Accepted Answer

A)  Not possible 
B) 
$$\left[ \begin{array} { c c c } 
3 & - 7 & 2 \
6 & - 24 & 24
\end{array} \right]$$ 
C) 
$\left[\begin{array}{rr}
3 & 6 \
-7 & -24 \
2 & 24
\end{array}\right]$ 
D) 
$\left[\begin{array}{rrr}
0 & -6 & 12 \
3 & -18 & 12
\end{array}\right]$ 
A)  Not possible 
B) 
$$\left[ \begin{array} { c c c } 
3 & - 7 & 2 \
6 & - 24 & 24
\end{array} \right]$$ 
C) 
$\left[\begin{array}{rr}
3 & 6 \
-7 & -24 \
2 & 24
\end{array}\right]$ 
D) 
$\left[\begin{array}{rrr}
0 & -6 & 12 \
3 & -18 & 12
\end{array}\right]$

Question 13

Determine the value of each variable.
-$$\left[ \begin{array} { l l } 
8 & 4 \
x & 0
\end{array} \right] = \left[ \begin{array} { r r } 
m - 4 & n + 4 \
5 & 0
\end{array} \right]$$

Accepted Answer

A)  $\mathrm { m } = 0 ; \mathrm { n } = 12 ; \mathrm { x } = 0$ 
B)  $m = 12 ; n = 0 ; x = 5$ 
C)  $m = - 12 ; n = - 0 ; x = - 5$ 
D)  $m = 8 ; n = 4 ; x = 5$ 
A)  $\mathrm { m } = 0 ; \mathrm { n } = 12 ; \mathrm { x } = 0$ 
B)  $m = 12 ; n = 0 ; x = 5$ 
C)  $m = - 12 ; n = - 0 ; x = - 5$ 
D)  $m = 8 ; n = 4 ; x = 5$

Question 14

Solve the system graphically.
-\[\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 7.82 \
x = 2 y - 5 \
\begin{aligned}
\text {

Accepted Answer

A)  } \approx ( - 2.97 , - 1.01 ) 	ext { and } \approx ( 6.31 , - 5.65 ) & 	ext { 
B)  } \approx ( - 6.31,5.65 ) 	ext { and } \approx ( 2.97,1.01 ) \
	ext { 
C)  } \approx ( - 6.31 , - 5.65 ) 	ext { and } \approx ( 2.97 , - 1.01 ) & 	ext { 
D)  } \approx ( - 2.97,1.01 ) 	ext { and } \approx ( 6.31,5.65 )
\end{aligned}
\end{array}\] 
A)  } \approx ( - 2.97 , - 1.01 ) 	ext { and } \approx ( 6.31 , - 5.65 ) & 	ext { 
B)  } \approx ( - 6.31,5.65 ) 	ext { and } \approx ( 2.97,1.01 ) \
	ext { 
C)  } \approx ( - 6.31 , - 5.65 ) 	ext { and } \approx ( 2.97 , - 1.01 ) & 	ext { 
D)  } \approx ( - 2.97,1.01 ) 	ext { and } \approx ( 6.31,5.65 )
\end{aligned}
\end{array}\]

Question 15

Graph the system of inequalities. Shade the region that represents the solution set.
-$\begin{array}{r}
x^{2}+y^{2} \leq 16 \
x+y \geq-1
\end{array}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Decide whether the ordered pair is a solution of the given system.
-$$\begin{array} { l } 
( 2,5 ) \
y = x ^ { 2 } + 2 x - 3 \
y = 4 x - 4
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 17

Find the indicated matrix.
-Let $C = \left[ \begin{array} { r } 1 \ - 3 \ 2 \end{array} \right]$ and $D = \left[ \begin{array} { r } - 1 \ 3 \ 2 \end{array} \right]$. Find $C - 3 D$

Accepted Answer

A) 
$\left[\begin{array}{r}
-2 \
6 \
-4
\end{array}\right]$ 
B) 
$\left[ \begin{array} { r } 4 \ - 6 \ 4 \end{array} \right]$ 
C) 
$\left[\begin{array}{r}
4 \
-12 \
-4
\end{array}\right]$ 
D) 
$\left[\begin{array}{r}
-4 \
12 \
4
\end{array}\right]$ 
A) 
$\left[\begin{array}{r}
-2 \
6 \
-4
\end{array}\right]$ 
B) 
$\left[ \begin{array} { r } 4 \ - 6 \ 4 \end{array} \right]$ 
C) 
$\left[\begin{array}{r}
4 \
-12 \
-4
\end{array}\right]$ 
D) 
$\left[\begin{array}{r}
-4 \
12 \
4
\end{array}\right]$

Question 18

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { l l } 
0 & - 3 \
4 & - 3
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { c c } 
- \frac { 1 } { 4 } & - \frac { 1 } { 4 } \
\frac { 1 } { 3 } & 0
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { r r } 
0 & \frac { 1 } { 4 } \
- \frac { 1 } { 3 } & - \frac { 1 } { 4 }
\end{array} \right]$$ 
C)  Inverse does not exist 
D) 
$$\left[ \begin{array} { l l } 
- \frac { 1 } { 4 } & \frac { 1 } { 4 } \
- \frac { 1 } { 3 } & 0
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { c c } 
- \frac { 1 } { 4 } & - \frac { 1 } { 4 } \
\frac { 1 } { 3 } & 0
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { r r } 
0 & \frac { 1 } { 4 } \
- \frac { 1 } { 3 } & - \frac { 1 } { 4 }
\end{array} \right]$$ 
C)  Inverse does not exist 
D) 
$$\left[ \begin{array} { l l } 
- \frac { 1 } { 4 } & \frac { 1 } { 4 } \
- \frac { 1 } { 3 } & 0
\end{array} \right]$$

Question 19

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix.
-Find a reduced row echelon form for the matrix.

Accepted Answer

The answer of Find a row echelon form or a...

Question 20

Find the indicated matrix.
-Let $B = \left[ \begin{array} { l l l l } - 1 & 2 & 4 & - 3 \end{array} \right]$. Find $- 4 B$.

Accepted Answer

A)  $\left[ \begin{array} { l l l l } - 3 & 0 & 2 & - 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } 4 & - 8 & - 16 & 12 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l l } - 4 & 8 & 16 & - 12 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } 4 & 2 & 4 & - 3 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l l l } - 3 & 0 & 2 & - 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } 4 & - 8 & - 16 & 12 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l l } - 4 & 8 & 16 & - 12 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } 4 & 2 & 4 & - 3 \end{array} \right]$

Determine which inequality matches the graph. -

Perform the indicated operation, if possible. - $\left[ \begin{array} { r r } - 1 & 0 \\5 & 2\end{array} \right] - \left[ \begin{array} { r r } - 1 & 5 \\3 & 1\end{array} \right]$

Find the partial fraction decomposition. - $\frac { 5 x - 2 } { x ^ { 3 } - 4 x } = \frac { A } { x } + \frac { B } { x + 2 } + \frac { C } { x - 2 }$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r r } - 8 & - 4 & - 7 & - 6 \\ 4 & 3 & 0 & 6 \\ 8 & 0 & 8 & 2 \end{array} \right]$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r } - 9 & - 3 & - 9 \\9 & - 6 & - 6\end{array} \right]$

Use the graph to estimate any solutions of the system. - y=-2+x- y=-3+x $Use the graph to estimate any solutions of the system. - \begin{array}{l} y=-2+x-x^{2} \\ y=-3+x \end{array} [ - 5,5 ] by [ - 5,5 ]$ $[ - 5,5 ]$ by $[ - 5,5 ]$

Determine the order of the matrix. - $\left[ \begin{array} { r r } 4 & 8 \\- 5 & - 1\end{array} \right]$

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l l } 0 & 0 & 0 & 7 \\9 & 8 & 8 & 4 \\7 & 7 & 4 & 8 \\1 & 4 & 7 & 2\end{array} \right]$

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Find the matrix product, if possible. - $\left[ \begin{array} { r r r } 5 & 1 & - 8 \\ - 2 & - 8 & 5 \\ - 4 & 2 & 4 \end{array} \right] \left[ \begin{array} { r r r } 5 & 8 & - 6 \\ - 5 & 6 & - 6 \\ 3 & 8 & - 9 \end{array} \right]$

Identify the element specified for the matrix. - $\left[ \begin{array} { r r r r r } - 6 & 1 & - 5 & 8 & 3 \\- 9 & - 8 & - 5 & - 7 & 3 \\5 & 0 & - 1 & - 2 & 3 \\- 3 & 5 & - 9 & 1 & 6\end{array} \right]$ a11

Find the matrix product, if possible. - $\left[ \begin{array} { r r } - 1 & 3 \\3 & 6\end{array} \right] \left[ \begin{array} { l l l } 0 & - 2 & 4 \\1 & - 3 & 2\end{array} \right]$

Determine the value of each variable. - $\left[ \begin{array} { l l } 8 & 4 \\x & 0\end{array} \right] = \left[ \begin{array} { r r } m - 4 & n + 4 \\5 & 0\end{array} \right]$

Solve the system graphically. - \[\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 7.82 \\ x = 2 y - 5 \\ \begin{aligned} \text {

Graph the system of inequalities. Shade the region that represents the solution set. - +\leq16 x+y\geq-1 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{array}{r} x^{2}+y^{2} \leq 16 \\ x+y \geq-1 \end{array}$

Decide whether the ordered pair is a solution of the given system. - (2,5) y=+2x-3 y=4x-4

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 1 \\ - 3 \\ 2 \end{array} \right]$ and $D = \left[ \begin{array} { r } - 1 \\ 3 \\ 2 \end{array} \right]$ . Find $C - 3 D$

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { l l } 0 & - 3 \\4 & - 3\end{array} \right]$

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix. -Find a reduced row echelon form for the matrix.

Find the indicated matrix. -Let $B = \left[ \begin{array} { l l l l } - 1 & 2 & 4 & - 3 \end{array} \right]$ . Find $- 4 B$ .

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Exam 7: Systems and Matrices

Determine which inequality matches the graph. -

Perform the indicated operation, if possible. - [−1052]−[−1531]\left[ \begin{array} { r r } - 1 & 0 \\5 & 2\end{array} \right] - \left[ \begin{array} { r r } - 1 & 5 \\3 & 1\end{array} \right][−15​02​]−[−13​51​]

Find the partial fraction decomposition. - 5x−2x3−4x=Ax+Bx+2+Cx−2\frac { 5 x - 2 } { x ^ { 3 } - 4 x } = \frac { A } { x } + \frac { B } { x + 2 } + \frac { C } { x - 2 }x3−4x5x−2​=xA​+x+2B​+x−2C​

Write the system of equations associated with the augmented matrix. Do not solve. - [−8−4−7−643068082]\left[ \begin{array} { r r r r } - 8 & - 4 & - 7 & - 6 \\ 4 & 3 & 0 & 6 \\ 8 & 0 & 8 & 2 \end{array} \right]​−848​−430​−708​−662​​

Write the system of equations associated with the augmented matrix. Do not solve. - [−9−3−99−6−6]\left[ \begin{array} { r r r } - 9 & - 3 & - 9 \\9 & - 6 & - 6\end{array} \right][−99​−3−6​−9−6​]

Use the graph to estimate any solutions of the system. - y=-2+x- y=-3+x [−5,5][ - 5,5 ][−5,5] by [−5,5][ - 5,5 ][−5,5]

Determine the order of the matrix. - [48−5−1]\left[ \begin{array} { r r } 4 & 8 \\- 5 & - 1\end{array} \right][4−5​8−1​]

Find the determinant of the given matrix. - [0007988477481472]\left[ \begin{array} { l l l l } 0 & 0 & 0 & 7 \\9 & 8 & 8 & 4 \\7 & 7 & 4 & 8 \\1 & 4 & 7 & 2\end{array} \right]​0971​0874​0847​7482​​