Solve the system in terms of the arbitrary variable x. -\[\begin{array} { l } x - 3 y + z = 35 \\ 3 x - y - z = 21 \end{array}\] $3 x - y - z = 21$

A) $\{ ( x , x - 14,3 x - 7 ) \}$ B) $\{ ( x , x - 14,2 x - 7 ) \}$ C) $\{ ( 0 , - 14 , - 7 ) \}$ D) $\{ ( x , x - 14,2 x ) \}$ A) $\{ ( x , x - 14,3 x - 7 ) \}$ B) $\{ ( x , x - 14,2 x - 7 ) \}$ C) $\{ ( 0 , - 14 , - 7 ) \}$ D) $\{ ( x , x - 14,2 x ) \}$

Solve the system. $\begin{array} { r } 4 x - 2 y - 3 z + 1 = 0 \\ 12 x - 2 y + 6 z - 4 = 0 \\ 4 y + 3 z - 3 = 0 \end{array}$

A) $\left\{ \left( - \frac { 1 } { 4 } , \frac { 1 } { 2 } , - \frac { 1 } { 3 } \right) \right\}$ B) $\left\{ \left( \frac { 1 } { 4 } , \frac { 1 } { 2 } , \frac { 1 } { 3 } \right) \right\}$ C) $\varnothing$ D) $\left\{ \left( - \frac { 1 } { 4 } , - \frac { 1 } { 2 } , \frac { 1 } { 3 } \right) \right\}$ A) $\left\{ \left( - \frac { 1 } { 4 } , \frac { 1 } { 2 } , - \frac { 1 } { 3 } \right) \right\}$ B) $\left\{ \left( \frac { 1 } { 4 } , \frac { 1 } { 2 } , \frac { 1 } { 3 } \right) \right\}$ C) $\varnothing$ D) $\left\{ \left( - \frac { 1 } { 4 } , - \frac { 1 } { 2 } , \frac { 1 } { 3 } \right) \right\}$

Write the augmented matrix for the system. Do not -\[\begin{aligned} 6 x + 9 y & = 96 \\ - 2 y & = - 16 \end{aligned}\]

A) $\left[ \begin{array} { r r | r } 96 & 9 & 6 \\ - 16 & 0 & - 2 \end{array} \right]$ B) $\left[ \begin{array} { r r | r } 6 & 9 & 96 \\ - 2 & - 16 & 0 \end{array} \right]$ C) $\left[ \begin{array} { r r | r } 6 & 9 & 96 \\ 0 & - 2 & - 16 \end{array} \right]$ D) $\left[ \begin{array} { r r | r } - 2 & 0 & - 16 \\ 6 & 9 & 9 \end{array} \right]$ A) $\left[ \begin{array} { r r | r } 96 & 9 & 6 \\ - 16 & 0 & - 2 \end{array} \right]$ B) $\left[ \begin{array} { r r | r } 6 & 9 & 96 \\ - 2 & - 16 & 0 \end{array} \right]$ C) $\left[ \begin{array} { r r | r } 6 & 9 & 96 \\ 0 & - 2 & - 16 \end{array} \right]$ D) $\left[ \begin{array} { r r | r } - 2 & 0 & - 16 \\ 6 & 9 & 9 \end{array} \right]$

Exam 6: Systems and Matrices

The perimeter of a triangle is 70 cm. The triangle is isosceles now, but if its base were lengthened by 7 cm and each leg were shortened by 4 cm, it would be equilateral. Find the length of the base of the original triangle.

(Multiple Choice)

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Question 441

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x-y+4z=14 3x+z=4 x+5y+z=14

(Multiple Choice)

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(74)

Question 442

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & - 1 & 3 \\1 & 0 & 5 \\2 & - 1 & 8\end{array} \right]$

(Multiple Choice)

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Question 443

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { l l l } 1 & 3 & 0 \\3 & 5 & 3 \\4 & 4 & 0\end{array} \right|$

(Multiple Choice)

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Question 444

Solve the system in terms of the arbitrary variable x. - x-3y+z=35 3x-y-z=21 $3 x - y - z = 21$

(Multiple Choice)

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Question 445

Solve the system. 4x-2y-3z+1=0 12x-2y+6z-4=0 4y+3z-3=0

(Multiple Choice)

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Question 446

Use the given row transformation to change the matrix as indicated. - $\left[\begin{array}{rr}5 & 3 \\10 & 7\end{array}\right] ;-2 \text { times row } 1 \text { added to row } 2$

(Multiple Choice)

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Question 447

Provide an appropriate response. -Consider the matrix $A = \left[ \begin{array} { r r r } - 9 & 6 & 2 \\- 1 & - 2 & 0 \\- 10 & 3 & 0\end{array} \right]$ Without using a calculator, determine whether A $- 1$ exists. Explain your reasoning

(Essay)

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Question 448

Find the partial fraction decomposition for the rational expression. $\frac { 3 } { x ^ { 2 } \left( x ^ { 2 } + 2 \right) }$

(Multiple Choice)

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Question 449

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

(Essay)

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Question 450

Evaluate the determinant. $\left| \begin{array} { l l l l } 0 & 0 & 0 & 2 \\3 & 8 & 2 & 5 \\4 & 1 & 2 & 5 \\7 & 2 & 6 & 3\end{array} \right|$

(Multiple Choice)

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Question 451

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 4x-y+4z=58 9x+3y+5z=130 3x-8y+z=-16

(Multiple Choice)

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Question 452

Write the augmented matrix for the system. Do not - 6x+9y =96 -2y =-16

(Multiple Choice)

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Question 453

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 2x+5y=-7 -6x-15y=21

(Multiple Choice)

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(75)

Question 454

Find the dimension of the matrix. - $\left[ \begin{array} { r r r } - 7 & 0 & 0 \\- 9 & - 7 & 0 \\- 2 & 4 & - 7\end{array} \right]$

(Multiple Choice)

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Question 455

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. 3+10=81 -4+9=9

(Essay)

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Question 456

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

(Multiple Choice)

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Question 457

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. xy=7 2-=7

(Multiple Choice)

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Question 458

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x+y<-2$

(Multiple Choice)

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Question 459

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r | r } - 4 & - 6 & 4 \\4 & - 7 & - 9\end{array} \right]$

(Multiple Choice)

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Question 460

The perimeter of a triangle is 70 cm. The triangle is isosceles now, but if its base were lengthened by 7 cm and each leg were shortened by 4 cm, it would be equilateral. Find the length of the base of the original triangle.

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x-y+4z=14 3x+z=4 x+5y+z=14

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & - 1 & 3 \\1 & 0 & 5 \\2 & - 1 & 8\end{array} \right]$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { l l l } 1 & 3 & 0 \\3 & 5 & 3 \\4 & 4 & 0\end{array} \right|$

Solve the system in terms of the arbitrary variable x. - x-3y+z=35 3x-y-z=21 $3 x - y - z = 21$

Solve the system. 4x-2y-3z+1=0 12x-2y+6z-4=0 4y+3z-3=0

Use the given row transformation to change the matrix as indicated. - $\left[\begin{array}{rr}5 & 3 \\10 & 7\end{array}\right] ;-2 \text { times row } 1 \text { added to row } 2$

Provide an appropriate response. -Consider the matrix $A = \left[ \begin{array} { r r r } - 9 & 6 & 2 \\- 1 & - 2 & 0 \\- 10 & 3 & 0\end{array} \right]$ Without using a calculator, determine whether A $- 1$ exists. Explain your reasoning

Find the partial fraction decomposition for the rational expression. $\frac { 3 } { x ^ { 2 } \left( x ^ { 2 } + 2 \right) }$

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Evaluate the determinant. $\left| \begin{array} { l l l l } 0 & 0 & 0 & 2 \\3 & 8 & 2 & 5 \\4 & 1 & 2 & 5 \\7 & 2 & 6 & 3\end{array} \right|$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 4x-y+4z=58 9x+3y+5z=130 3x-8y+z=-16

Write the augmented matrix for the system. Do not - 6x+9y =96 -2y =-16

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 2x+5y=-7 -6x-15y=21

Find the dimension of the matrix. - $\left[ \begin{array} { r r r } - 7 & 0 & 0 \\- 9 & - 7 & 0 \\- 2 & 4 & - 7\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. 3+10=81 -4+9=9

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. xy=7 2-=7

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x+y<-2$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r | r } - 4 & - 6 & 4 \\4 & - 7 & - 9\end{array} \right]$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 6: Systems and Matrices

The perimeter of a triangle is 70 cm. The triangle is isosceles now, but if its base were lengthened by 7 cm and each leg were shortened by 4 cm, it would be equilateral. Find the length of the base of the original triangle.

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x-y+4z=14 3x+z=4 x+5y+z=14

Find the inverse, if it exists, for the matrix. - [1−131052−18]\left[ \begin{array} { l l l } 1 & - 1 & 3 \\1 & 0 & 5 \\2 & - 1 & 8\end{array} \right]​112​−10−1​358​​

Use a graphing calculator to find the value of the determinant. - ∣130353440∣\left| \begin{array} { l l l } 1 & 3 & 0 \\3 & 5 & 3 \\4 & 4 & 0\end{array} \right|​134​354​030​​

Solve the system in terms of the arbitrary variable x. - x-3y+z=35 3x-y-z=21 3x−y−z=213 x - y - z = 213x−y−z=21

Solve the system. 4x-2y-3z+1=0 12x-2y+6z-4=0 4y+3z-3=0

Use the given row transformation to change the matrix as indicated. - [53107];−2 times row 1 added to row 2\left[\begin{array}{rr}5 & 3 \\10 & 7\end{array}\right] ;-2 \text { times row } 1 \text { added to row } 2[510​37​];−2 times row 1 added to row 2

Find the partial fraction decomposition for the rational expression. 3x2(x2+2)\frac { 3 } { x ^ { 2 } \left( x ^ { 2 } + 2 \right) }x2(x2+2)3​

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Evaluate the determinant. ∣0002382541257263∣\left| \begin{array} { l l l l } 0 & 0 & 0 & 2 \\3 & 8 & 2 & 5 \\4 & 1 & 2 & 5 \\7 & 2 & 6 & 3\end{array} \right|​0347​0812​0226​2553​​

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 4x-y+4z=58 9x+3y+5z=130 3x-8y+z=-16

Write the augmented matrix for the system. Do not - 6x+9y =96 -2y =-16

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 2x+5y=-7 -6x-15y=21

Find the dimension of the matrix. - [−700−9−70−24−7]\left[ \begin{array} { r r r } - 7 & 0 & 0 \\- 9 & - 7 & 0 \\- 2 & 4 & - 7\end{array} \right]​−7−9−2​0−74​00−7​​

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. 3+10=81 -4+9=9

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. xy=7 2-=7

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. x+y<−2x+y<-2x+y<−2

Write the system of equations associated with the augmented matrix. Do not solve. - [−4−644−7−9]\left[ \begin{array} { r r | r } - 4 & - 6 & 4 \\4 & - 7 & - 9\end{array} \right][−44​−6−7​4−9​]

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & - 1 & 3 \\1 & 0 & 5 \\2 & - 1 & 8\end{array} \right]$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { l l l } 1 & 3 & 0 \\3 & 5 & 3 \\4 & 4 & 0\end{array} \right|$

Solve the system in terms of the arbitrary variable x. - x-3y+z=35 3x-y-z=21 $3 x - y - z = 21$

Use the given row transformation to change the matrix as indicated. - $\left[\begin{array}{rr}5 & 3 \\10 & 7\end{array}\right] ;-2 \text { times row } 1 \text { added to row } 2$

Find the partial fraction decomposition for the rational expression. $\frac { 3 } { x ^ { 2 } \left( x ^ { 2 } + 2 \right) }$

Evaluate the determinant. $\left| \begin{array} { l l l l } 0 & 0 & 0 & 2 \\3 & 8 & 2 & 5 \\4 & 1 & 2 & 5 \\7 & 2 & 6 & 3\end{array} \right|$

Find the dimension of the matrix. - $\left[ \begin{array} { r r r } - 7 & 0 & 0 \\- 9 & - 7 & 0 \\- 2 & 4 & - 7\end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x+y<-2$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r | r } - 4 & - 6 & 4 \\4 & - 7 & - 9\end{array} \right]$