Question 1

Solve the system by elimination.
$\begin{array} { l } 
\frac { x + 4 } { 5 } + \frac { 2 y - x } { 10 } = 2 \
\frac { x + 2 } { 4 } + \frac { 3 y + 4 } { 5 } = - 3
\end{array}$

Accepted Answer

A)  $\{ ( 158 , - 73 ) \}$ 
B)  $\phi$ 
C)  $\{ ( - 14,13 ) \}$ 
D)  $\{ ( - 73,158 ) \}$ 
A)  $\{ ( 158 , - 73 ) \}$ 
B)  $\phi$ 
C)  $\{ ( - 14,13 ) \}$ 
D)  $\{ ( - 73,158 ) \}$

Question 2

The sum of the squares of the digits of a positive two-digit number is 61, and the tens digit is 1 more than the units digit. Find the number.

Accepted Answer

A)  65 
B)  45 
C)  56 
D)  54 
A)  65 
B)  45 
C)  56 
D)  54

Question 3

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$2 x - y = 4$$
$- 4 x + 2 y = - 8$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ ( x , 4 - 2 x ) \}$ 
C)  $\{ ( x , 4 x - 4 ) \}$ 
D)  $\{ ( x , 2 x - 4 ) \}$ 
A)  $\varnothing$ 
B)  $\{ ( x , 4 - 2 x ) \}$ 
C)  $\{ ( x , 4 x - 4 ) \}$ 
D)  $\{ ( x , 2 x - 4 ) \}$

Question 4

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } 
x y = 1 \
28 x - y = 3
\end{array}$

Accepted Answer

A)  $\left\{ \left( - \frac { 1 } { 7 } , - 7 \right) , \left( \frac { 1 } { 4 } , 4 \right) \right\}$ 
B)  $\left\{ \left( \frac { 1 } { 4 } , 4 \right) \right\}$ 
C)  $\{ ( 7 , - 7 ) , ( - 4,4 ) \}$ 
D)  $\left\{ \left( - 7 , - \frac { 1 } { 7 } \right) , \left( 4 , \frac { 1 } { 4 } \right) \right\}$ 
A)  $\left\{ \left( - \frac { 1 } { 7 } , - 7 \right) , \left( \frac { 1 } { 4 } , 4 \right) \right\}$ 
B)  $\left\{ \left( \frac { 1 } { 4 } , 4 \right) \right\}$ 
C)  $\{ ( 7 , - 7 ) , ( - 4,4 ) \}$ 
D)  $\left\{ \left( - 7 , - \frac { 1 } { 7 } \right) , \left( 4 , \frac { 1 } { 4 } \right) \right\}$

Question 5

Find the value of the determinant.
$\left| \begin{array} { l l } 
a & b \
b & a
\end{array} \right|$

Accepted Answer

A)   2ab 
B)  $a ^ { 2 } + b ^ { 2 }$ 
C)  $a ^ { 2 } - b ^ { 2 }$ 
D)  0 
A)   2ab 
B)  $a ^ { 2 } + b ^ { 2 }$ 
C)  $a ^ { 2 } - b ^ { 2 }$ 
D)  0

Question 6

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
x - 2 y = 8 \
- 3 x + 6 y = - 24
\end{array}$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left. \left\{ x , \frac { x } { 6 } - 4 \right\} \right\}$ 
C)  $\left. \left\{ x , \frac { x } { 2 } - 4 \right\} \right\}$ 
D)  $\left\{ \left\{ x , 4 - \frac { x } { 2 } \right) \right\}$ 
A)  $\varnothing$ 
B)  $\left. \left\{ x , \frac { x } { 6 } - 4 \right\} \right\}$ 
C)  $\left. \left\{ x , \frac { x } { 2 } - 4 \right\} \right\}$ 
D)  $\left\{ \left\{ x , 4 - \frac { x } { 2 } \right) \right\}$

Question 7

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities.
-$y \leq x^{2}+5$

Accepted Answer

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

Question 8

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { r } 
3 x + 5 y = - 10 \
- 3 x - 6 y = 9
\end{array}$$

Accepted Answer

A)  $\{ ( - 5,1 ) \}$ 
B)  $\{ ( 5 , - 1 ) \}$ 
C)  $\{ ( - 1,5 ) \}$ 
D)  $\{ ( 1 , - 5 ) \}$ 
A)  $\{ ( - 5,1 ) \}$ 
B)  $\{ ( 5 , - 1 ) \}$ 
C)  $\{ ( - 1,5 ) \}$ 
D)  $\{ ( 1 , - 5 ) \}$

Question 9

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { l l l } 
7 & - 5 & 2 \
14 & - 9 & 4 \
7 & - 4 & 2
\end{array} \right]$$

Accepted Answer

A)  The inverse does not exist. 
B) 
$$\left[ \begin{array} { l l l } 
7 & 14 & 7 \
- 5 & - 9 & - 4 \
2 & 4 & 2
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { l l l } 
\frac { 1 } { 7 } & \frac { 1 } { 7 } & - \frac { 5 } { 2 } \
\frac { 1 } { 2 } & \frac { 10 } { 9 } & \frac { 7 } { 4 } \
1 & - \frac { 1 } { 2 } & \frac { 1 } { 2 }
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c c } 
\frac { 1 } { 7 } & \frac { 1 } { 14 } & \frac { 1 } { 2 } \
\frac { 1 } { 14 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } \
\frac { 1 } { 7 } & - \frac { 1 } { 4 } & \frac { 1 } { 2 }
\end{array} \right]$$ 
A)  The inverse does not exist. 
B) 
$$\left[ \begin{array} { l l l } 
7 & 14 & 7 \
- 5 & - 9 & - 4 \
2 & 4 & 2
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { l l l } 
\frac { 1 } { 7 } & \frac { 1 } { 7 } & - \frac { 5 } { 2 } \
\frac { 1 } { 2 } & \frac { 10 } { 9 } & \frac { 7 } { 4 } \
1 & - \frac { 1 } { 2 } & \frac { 1 } { 2 }
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c c } 
\frac { 1 } { 7 } & \frac { 1 } { 14 } & \frac { 1 } { 2 } \
\frac { 1 } { 14 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } \
\frac { 1 } { 7 } & - \frac { 1 } { 4 } & \frac { 1 } { 2 }
\end{array} \right]$$

Question 10

Find the values of the variables for which the statement is true, if possible.
-$\left[ \begin{array} { r r } 8 & - 1 \ 4 & 5 \end{array} \right] = \left[ \begin{array} { r r } x & - 1 \ y & z \end{array} \right]$

Accepted Answer

A)  $x = 8 ; y = 4 ; z = 5$ 
B)  $x = 4 ; y = 5 ; z = 8$ 
C)  $x = - 8 ; y = 5 ; z = 4$ 
D)  $x = - 8 ; y = - 4 ; z = - 5$ 
A)  $x = 8 ; y = 4 ; z = 5$ 
B)  $x = 4 ; y = 5 ; z = 8$ 
C)  $x = - 8 ; y = 5 ; z = 4$ 
D)  $x = - 8 ; y = - 4 ; z = - 5$

Question 11

Provide an appropriate response.
-Indicate whether the following statement is If every element of a $14 \times 14$ matrix is multiplied by -3,
the determinant of the new matrix is -3 times the determinant of the original matrix.

Accepted Answer

A) True 
 B)False

Question 12

Perform the operation or operations when possible.
-$\left[ \begin{array} { r r } - 8 & 2 \ 9 & 4 \ 8 & - 1 \end{array} \right] + \left[ \begin{array} { r r } 8 & - 4 \ - 2 & - 2 \ 7 & 2 \end{array} \right]$

Accepted Answer

A) 
$\left[ \begin{array} { r r } - 16 & 6 \ 11 & 6 \ 1 & - 2 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 0 & - 2 \ - 7 & 4 \ 15 & - 1 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 0 & 4 \ 7 & 2 \ 15 & 1 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } 0 & - 2 \ 7 & 2 \ 15 & 1 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r r } - 16 & 6 \ 11 & 6 \ 1 & - 2 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 0 & - 2 \ - 7 & 4 \ 15 & - 1 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 0 & 4 \ 7 & 2 \ 15 & 1 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } 0 & - 2 \ 7 & 2 \ 15 & 1 \end{array} \right]$

Question 13

Solve the system by elimination.
-$$\begin{array} { c } 
x - 3 y = - 8 \
6 x - 4 y = 22
\end{array}$$

Accepted Answer

A)  $\{ ( - 7,6 ) \}$ 
B)  $\{ ( 7,5 ) \}$ 
C)  $\{ ( 6,6 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( - 7,6 ) \}$ 
B)  $\{ ( 7,5 ) \}$ 
C)  $\{ ( 6,6 ) \}$ 
D)  $\varnothing$

Question 14

Find the partial fraction decomposition for the rational expression.
$\frac { 10 x ^ { 2 } - 23 x + 4 } { ( x - 4 ) \left( x ^ { 2 } + 2 \right) }$

Accepted Answer

A)  $\frac { 6 x + 1 } { x ^ { 2 } + 2 } + \frac { 4 } { x - 4 }$ 
B)  $\frac { 6 x - 1 } { x ^ { 2 } + 2 } + \frac { - 4 } { x - 4 }$ 
C)  $\frac { - ( 6 x + 1 ) } { x ^ { 2 } + 2 } + \frac { 4 } { x - 4 }$ 
D)  $\frac { 6 x + 4 } { x ^ { 2 } + 2 } + \frac { 1 } { x - 4 }$ 
A)  $\frac { 6 x + 1 } { x ^ { 2 } + 2 } + \frac { 4 } { x - 4 }$ 
B)  $\frac { 6 x - 1 } { x ^ { 2 } + 2 } + \frac { - 4 } { x - 4 }$ 
C)  $\frac { - ( 6 x + 1 ) } { x ^ { 2 } + 2 } + \frac { 4 } { x - 4 }$ 
D)  $\frac { 6 x + 4 } { x ^ { 2 } + 2 } + \frac { 1 } { x - 4 }$

Question 15

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r r r } 
4 & - 2 & 0 & 3 \
12 & - 4 & 0 & 6 \
6 & - 8 & 0 & 9 \
0 & 0 & - 6 & 0
\end{array} \right]$$

Accepted Answer

A)  The inverse does not exist. 
B) 
$$\left[ \begin{array} { r r r r } 
- \frac { 1 } { 2 } & 3 & 0 & 3 \
\frac { 1 } { 4 } & - \frac { 3 } { 4 } & 0 & - \frac { 5 } { 6 } \
0 & - \frac { 1 } { 2 } & 0 & - \frac { 1 } { 3 } \
0 & 0 & - \frac { 1 } { 6 } & 0
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r r } 
- \frac { 1 } { 2 } & \frac { 1 } { 4 } & 0 & 0 \
3 & - \frac { 3 } { 4 } & - \frac { 1 } { 2 } & 0 \
0 & 0 & 0 & - \frac { 1 } { 6 } \
3 & - \frac { 5 } { 6 } & - \frac { 1 } { 3 } & 0
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 4 } & - \frac { 1 } { 2 } & 0 & \frac { 1 } { 3 } \
\frac { 1 } { 12 } & - \frac { 1 } { 4 } & 0 & \frac { 1 } { 6 } \
\frac { 1 } { 6 } & - \frac { 1 } { 8 } & 0 & \frac { 1 } { 9 } \
0 & 0 & - \frac { 1 } { 6 } & 0
\end{array} \right]$$ 
A)  The inverse does not exist. 
B) 
$$\left[ \begin{array} { r r r r } 
- \frac { 1 } { 2 } & 3 & 0 & 3 \
\frac { 1 } { 4 } & - \frac { 3 } { 4 } & 0 & - \frac { 5 } { 6 } \
0 & - \frac { 1 } { 2 } & 0 & - \frac { 1 } { 3 } \
0 & 0 & - \frac { 1 } { 6 } & 0
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r r } 
- \frac { 1 } { 2 } & \frac { 1 } { 4 } & 0 & 0 \
3 & - \frac { 3 } { 4 } & - \frac { 1 } { 2 } & 0 \
0 & 0 & 0 & - \frac { 1 } { 6 } \
3 & - \frac { 5 } { 6 } & - \frac { 1 } { 3 } & 0
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 4 } & - \frac { 1 } { 2 } & 0 & \frac { 1 } { 3 } \
\frac { 1 } { 12 } & - \frac { 1 } { 4 } & 0 & \frac { 1 } { 6 } \
\frac { 1 } { 6 } & - \frac { 1 } { 8 } & 0 & \frac { 1 } { 9 } \
0 & 0 & - \frac { 1 } { 6 } & 0
\end{array} \right]$$

Question 16

Solve the system by elimination.
-6x - 6y=18
2x - 4y=12

Accepted Answer

A)  $\{ ( - 1 , - 2 ) \}$ 
B)    
C)  $\{ ( 0 , - 3 ) \}$ 
D)  $\{ ( 0 , - 2 ) \}$ 
A)  $\{ ( - 1 , - 2 ) \}$ 
B)    
C)  $\{ ( 0 , - 3 ) \}$ 
D)  $\{ ( 0 , - 2 ) \}$

Question 17

Graph the solution set of the system of inequalities.
-$\begin{array}{c}
x+2 y \leq 2 \
x+y \geq 0
\end{array}$

Accepted Answer

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

Question 18

Find the dimension of the matrix.
-$$\left[ \begin{array} { r r r r r } 
- 6 & 1 & - 7 & 8 & - 4 \
- 1 & 9 & 6 & - 7 & - 8 \
7 & 2 & - 8 & 6 & 1
\end{array} \right]$$

Accepted Answer

A)  $3 \times 5$ 
B)  $- 6,1 , - 7,8 , - 4 , - 1,7$ 
C)  15 
D)  $5 \times 3$ 
A)  $3 \times 5$ 
B)  $- 6,1 , - 7,8 , - 4 , - 1,7$ 
C)  15 
D)  $5 \times 3$

Question 19

If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
6 x + 2 y - z = - 2 \
4 x - y + 2 z = 1 \
- 12 x - 4 y + 2 z = 0
\end{array}$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ ( x , - 1 - 3 x , - 2 - 6 x ) \}$ 
C)  $\left\{ \left( x , \frac { 1 } { 2 } - 2 x , 4 x - 1 \right) \right\}$ 
D)  $\{ ( 0,0 ) \}$ 
A)  $\varnothing$ 
B)  $\{ ( x , - 1 - 3 x , - 2 - 6 x ) \}$ 
C)  $\left\{ \left( x , \frac { 1 } { 2 } - 2 x , 4 x - 1 \right) \right\}$ 
D)  $\{ ( 0,0 ) \}$

Question 20

Choose the one alternative that best completes the statement or answers the question.
Graph the inequality.
$x-y>-5$

Accepted Answer

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

Solve the system by elimination. +=2 +=-3

The sum of the squares of the digits of a positive two-digit number is 61, and the tens digit is 1 more than the units digit. Find the number.

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - $2 x - y = 4$ $- 4 x + 2 y = - 8$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. xy=1 28x-y=3

Find the value of the determinant. $\left| \begin{array} { l l } a & b \\b & a\end{array} \right|$

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - x-2y=8 -3x+6y=-24

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - $y \leq x^{2}+5$ $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y \leq x^{2}+5$

Solve the system by using the inverse of the coefficient matrix. - 3x+5y=-10 -3x-6y=9

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 7 & - 5 & 2 \\14 & - 9 & 4 \\7 & - 4 & 2\end{array} \right]$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { r r } 8 & - 1 \\ 4 & 5 \end{array} \right] = \left[ \begin{array} { r r } x & - 1 \\ y & z \end{array} \right]$

Provide an appropriate response. -Indicate whether the following statement is If every element of a $14 \times 14$ matrix is multiplied by -3, the determinant of the new matrix is -3 times the determinant of the original matrix.

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 8 & 2 \\ 9 & 4 \\ 8 & - 1 \end{array} \right] + \left[ \begin{array} { r r } 8 & - 4 \\ - 2 & - 2 \\ 7 & 2 \end{array} \right]$

Solve the system by elimination. - x-3y=-8 6x-4y=22

Find the partial fraction decomposition for the rational expression. $\frac { 10 x ^ { 2 } - 23 x + 4 } { ( x - 4 ) \left( x ^ { 2 } + 2 \right) }$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 4 & - 2 & 0 & 3 \\12 & - 4 & 0 & 6 \\6 & - 8 & 0 & 9 \\0 & 0 & - 6 & 0\end{array} \right]$

Solve the system by elimination. -6x - 6y=18 2x - 4y=12

Graph the solution set of the system of inequalities. - x+2y\leq2 x+y\geq0 $Graph the solution set of the system of inequalities. - \begin{array}{c} x+2 y \leq 2 \\ x+y \geq 0 \end{array}$

Find the dimension of the matrix. - $\left[ \begin{array} { r r r r r } - 6 & 1 & - 7 & 8 & - 4 \\- 1 & 9 & 6 & - 7 & - 8 \\7 & 2 & - 8 & 6 & 1\end{array} \right]$

If the system has infinitely many solutions, write the solution set with x arbitrary. - 6x+2y-z=-2 4x-y+2z=1 -12x-4y+2z=0

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x-y>-5$

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

Solve the system by elimination. +=2 +=-3

The sum of the squares of the digits of a positive two-digit number is 61, and the tens digit is 1 more than the units digit. Find the number.

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 2x−y=42 x - y = 42x−y=4 −4x+2y=−8- 4 x + 2 y = - 8−4x+2y=−8

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. xy=1 28x-y=3

Find the value of the determinant. ∣abba∣\left| \begin{array} { l l } a & b \\b & a\end{array} \right|​ab​ba​​

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - x-2y=8 -3x+6y=-24

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y≤x2+5y \leq x^{2}+5y≤x2+5

Solve the system by using the inverse of the coefficient matrix. - 3x+5y=-10 -3x-6y=9

Find the inverse, if it exists, for the matrix. - [7−5214−947−42]\left[ \begin{array} { l l l } 7 & - 5 & 2 \\14 & - 9 & 4 \\7 & - 4 & 2\end{array} \right]​7147​−5−9−4​242​​

Find the values of the variables for which the statement is true, if possible. - [8−145]=[x−1yz]\left[ \begin{array} { r r } 8 & - 1 \\ 4 & 5 \end{array} \right] = \left[ \begin{array} { r r } x & - 1 \\ y & z \end{array} \right][84​−15​]=[xy​−1z​]

Provide an appropriate response. -Indicate whether the following statement is If every element of a 14×1414 \times 1414×14 matrix is multiplied by -3, the determinant of the new matrix is -3 times the determinant of the original matrix.

Perform the operation or operations when possible. - [−82948−1]+[8−4−2−272]\left[ \begin{array} { r r } - 8 & 2 \\ 9 & 4 \\ 8 & - 1 \end{array} \right] + \left[ \begin{array} { r r } 8 & - 4 \\ - 2 & - 2 \\ 7 & 2 \end{array} \right]​−898​24−1​​+​8−27​−4−22​​

Solve the system by elimination. - x-3y=-8 6x-4y=22

Find the partial fraction decomposition for the rational expression. 10x2−23x+4(x−4)(x2+2)\frac { 10 x ^ { 2 } - 23 x + 4 } { ( x - 4 ) \left( x ^ { 2 } + 2 \right) }(x−4)(x2+2)10x2−23x+4​

Find the inverse, if it exists, for the matrix. - [4−20312−4066−80900−60]\left[ \begin{array} { r r r r } 4 & - 2 & 0 & 3 \\12 & - 4 & 0 & 6 \\6 & - 8 & 0 & 9 \\0 & 0 & - 6 & 0\end{array} \right]​41260​−2−4−80​000−6​3690​​

Solve the system by elimination. -6x - 6y=18 2x - 4y=12

Graph the solution set of the system of inequalities. - x+2y\leq2 x+y\geq0

Find the dimension of the matrix. - [−61−78−4−196−7−872−861]\left[ \begin{array} { r r r r r } - 6 & 1 & - 7 & 8 & - 4 \\- 1 & 9 & 6 & - 7 & - 8 \\7 & 2 & - 8 & 6 & 1\end{array} \right]​−6−17​192​−76−8​8−76​−4−81​​

If the system has infinitely many solutions, write the solution set with x arbitrary. - 6x+2y-z=-2 4x-y+2z=1 -12x-4y+2z=0

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. x−y>−5x-y>-5x−y>−5

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

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - $2 x - y = 4$ $- 4 x + 2 y = - 8$

Find the value of the determinant. $\left| \begin{array} { l l } a & b \\b & a\end{array} \right|$

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - $y \leq x^{2}+5$ $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y \leq x^{2}+5$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 7 & - 5 & 2 \\14 & - 9 & 4 \\7 & - 4 & 2\end{array} \right]$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { r r } 8 & - 1 \\ 4 & 5 \end{array} \right] = \left[ \begin{array} { r r } x & - 1 \\ y & z \end{array} \right]$

Provide an appropriate response. -Indicate whether the following statement is If every element of a $14 \times 14$ matrix is multiplied by -3, the determinant of the new matrix is -3 times the determinant of the original matrix.

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 8 & 2 \\ 9 & 4 \\ 8 & - 1 \end{array} \right] + \left[ \begin{array} { r r } 8 & - 4 \\ - 2 & - 2 \\ 7 & 2 \end{array} \right]$

Find the partial fraction decomposition for the rational expression. $\frac { 10 x ^ { 2 } - 23 x + 4 } { ( x - 4 ) \left( x ^ { 2 } + 2 \right) }$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 4 & - 2 & 0 & 3 \\12 & - 4 & 0 & 6 \\6 & - 8 & 0 & 9 \\0 & 0 & - 6 & 0\end{array} \right]$

Graph the solution set of the system of inequalities. - x+2y\leq2 x+y\geq0 $Graph the solution set of the system of inequalities. - \begin{array}{c} x+2 y \leq 2 \\ x+y \geq 0 \end{array}$

Find the dimension of the matrix. - $\left[ \begin{array} { r r r r r } - 6 & 1 & - 7 & 8 & - 4 \\- 1 & 9 & 6 & - 7 & - 8 \\7 & 2 & - 8 & 6 & 1\end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x-y>-5$