Question 1

Solve the system of linear equations.
$$\left\{ \begin{aligned}
2 x - 2 y + 3 z & = - 21 \
2 x + z & = - 11 \
- 2 x + 4 y - 4 z & = 28
\end{aligned} \right.$$

Accepted Answer

A)  $( 3 , - 3,4 )$ 
B)  $( - 4,2 , - 3 )$ 
C)  $( 2 , - 3 , - 4 )$ 
D)  $( - 3,4,3 )$ 
E)  $( - 4,2,6 )$ 
A)  $( 3 , - 3,4 )$ 
B)  $( - 4,2 , - 3 )$ 
C)  $( 2 , - 3 , - 4 )$ 
D)  $( - 3,4,3 )$ 
E)  $( - 4,2,6 )$

Question 2

Write the partial fraction decomposition of the rational expression.
$$\frac { 5 } { x ^ { 2 } + 10 x + 16 }$$

Accepted Answer

A)  $\frac { 5 } { 6 } \left( \frac { 1 } { x - 2 } - \frac { 1 } { x - 8 } \right)$ 
B)  $\frac { 5 } { 6 } \left( \frac { 1 } { x + 2 } - \frac { 1 } { x + 8 } \right)$ 
C)  $\frac { 5 } { 6 } \left( \frac { 1 } { x + 8 } - \frac { 1 } { x + 2 } \right)$ 
D)  $\frac { 5 } { x ^ { 2 } } + \frac { 1 } { 2 x } + \frac { 5 } { 16 }$ 
E)  $\frac { 5 } { x ^ { 2 } + 10 x + 16 }$ 
A)  $\frac { 5 } { 6 } \left( \frac { 1 } { x - 2 } - \frac { 1 } { x - 8 } \right)$ 
B)  $\frac { 5 } { 6 } \left( \frac { 1 } { x + 2 } - \frac { 1 } { x + 8 } \right)$ 
C)  $\frac { 5 } { 6 } \left( \frac { 1 } { x + 8 } - \frac { 1 } { x + 2 } \right)$ 
D)  $\frac { 5 } { x ^ { 2 } } + \frac { 1 } { 2 x } + \frac { 5 } { 16 }$ 
E)  $\frac { 5 } { x ^ { 2 } + 10 x + 16 }$

Question 3

Identify the elementary row operation being performed to obtain the new rowequivalent matrix.
$\begin{array} { l r } \text { Original Matrix } & \text { New Row-Equivalent Matrix } \ { \left[ \begin{array} { c c c } 7 & 6 & 6 \ 1 & 4 & - 6 \end{array} \right] } & { \left[ \begin{array} { c c c } 12 & 26 & - 24 \ 1 & 4 & - 6 \end{array} \right] } \end{array}$

Accepted Answer

A)  Add 5 times $R _ { 1 }$ to $R _ { 2 }$. 
B)  Add $- 5$ times $R _ { 2 }$ to $R _ { 1 }$. 
C)  Add $- 5$ times $R _ { 1 }$ to $R _ { 2 }$. 
D)  Add 5 times $R _ { 1 }$ to $R _ { 1 }$. 
E)  Add 5 times $R _ { 2 }$ to $R _ { 1 }$. 
A)  Add 5 times $R _ { 1 }$ to $R _ { 2 }$. 
B)  Add $- 5$ times $R _ { 2 }$ to $R _ { 1 }$. 
C)  Add $- 5$ times $R _ { 1 }$ to $R _ { 2 }$. 
D)  Add 5 times $R _ { 1 }$ to $R _ { 1 }$. 
E)  Add 5 times $R _ { 2 }$ to $R _ { 1 }$.

Question 4

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 5

An object moving vertically is at the given heights at the specified times. Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { o } t + s _ { o }$ for the object.
At $t = 1$ second, $s = 198$ feet
At $t = 2$ seconds, $s = 182$ feet
At $t = 3$ seconds, $s = 134$ feet

Accepted Answer

A)  $s = - 32 t ^ { 2 } + 32 t + 198$ 
B)  $s = - 16 t ^ { 2 } + 32 t - 182$ 
C)  $s = - 16 t ^ { 2 } + 32 t + 182$ 
D)  $s = - 8 t ^ { 2 } + 2 t - 182$ 
E)  $s = - 16 t ^ { 2 } - 32 t + 198$ 
A)  $s = - 32 t ^ { 2 } + 32 t + 198$ 
B)  $s = - 16 t ^ { 2 } + 32 t - 182$ 
C)  $s = - 16 t ^ { 2 } + 32 t + 182$ 
D)  $s = - 8 t ^ { 2 } + 2 t - 182$ 
E)  $s = - 16 t ^ { 2 } - 32 t + 198$

Question 6

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
$$\left\{ \begin{array} { l } 
7 x - 3 y - 9 z = 22 \
2 x + y + 3 z = - 3 \
2 x - 7 y - 3 z = - 17
\end{array} \right.$$

Accepted Answer

A)  $x = - 1 , y = - 4 , z = - 3$ 
B)  $x = 1 , y = - 4 , z = - 3$ 
C)  $x = 1 , y = 4 , z = - 3$ 
D)  $x = 4 , y = - 1 , z = 3$ 
E)  no solution 
A)  $x = - 1 , y = - 4 , z = - 3$ 
B)  $x = 1 , y = - 4 , z = - 3$ 
C)  $x = 1 , y = 4 , z = - 3$ 
D)  $x = 4 , y = - 1 , z = 3$ 
E)  no solution

Question 7

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

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 8

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

Question 9

Solve the system by the method of substitution.
$$\left\{ \begin{aligned}
x ^ { 2 } + y ^ { 2 } & = 625 \
7 x - 24 y & = 0
\end{aligned} \right.$$

Accepted Answer

A)  $( 24,7 ) , ( - 24 , - 7 )$ 
B)  $( 24,7 )$ 
C)  $( 24,7 ) , ( - 24,7 ) , ( - 24 , - 7 ) , ( 24 , - 7 )$ 
D)  $( 7,24 ) , ( 7 , - 24 )$ 
E)  no real solution 
A)  $( 24,7 ) , ( - 24 , - 7 )$ 
B)  $( 24,7 )$ 
C)  $( 24,7 ) , ( - 24,7 ) , ( - 24 , - 7 ) , ( 24 , - 7 )$ 
D)  $( 7,24 ) , ( 7 , - 24 )$ 
E)  no real solution

Question 10

Find the minor $M _ { 13 }$ and its cofactor $C _ { 13 }$ of the matrix $\left[ \begin{array} { c c c } - 9 & 6 & - 24 \ 9 & - 6 & 18 \ - 3 & 9 & - 18 \end{array} \right]$

Accepted Answer

A)  $M _ { 13 } = \left| \begin{array} { r r } - 9 & - 24 \ - 3 & - 18 \end{array} \right| = 90$
$$C _ { 13 } = - 90$$ 
B)  $M _ { 13 } = \left| \begin{array} { c c } 6 & - 24 \ - 6 & 18 \end{array} \right| = - 36$
$$C _ { 13 } = - 36$$ 
C)  $M _ { 13 } = \left| \begin{array} { c c } 9 & - 6 \ - 3 & 9 \end{array} \right| = 63$
$$C _ { 13 } = - 63$$ 
D) 
$$\begin{array} { l } 
M _ { 13 } = \left| \begin{array} { c c } 
6 & - 24 \
- 6 & 18
\end{array} \right| = - 36 \
C _ { 13 } = 36
\end{array}$$ 
E) 
$$\begin{array} { l } 
M _ { 13 } = \left| \begin{array} { c c } 
9 & - 6 \
- 3 & 9
\end{array} \right| = 63 \
C _ { 13 } = 63
\end{array}$$ 
A)  $M _ { 13 } = \left| \begin{array} { r r } - 9 & - 24 \ - 3 & - 18 \end{array} \right| = 90$
$$C _ { 13 } = - 90$$ 
B)  $M _ { 13 } = \left| \begin{array} { c c } 6 & - 24 \ - 6 & 18 \end{array} \right| = - 36$
$$C _ { 13 } = - 36$$ 
C)  $M _ { 13 } = \left| \begin{array} { c c } 9 & - 6 \ - 3 & 9 \end{array} \right| = 63$
$$C _ { 13 } = - 63$$ 
D) 
$$\begin{array} { l } 
M _ { 13 } = \left| \begin{array} { c c } 
6 & - 24 \
- 6 & 18
\end{array} \right| = - 36 \
C _ { 13 } = 36
\end{array}$$ 
E) 
$$\begin{array} { l } 
M _ { 13 } = \left| \begin{array} { c c } 
9 & - 6 \
- 3 & 9
\end{array} \right| = 63 \
C _ { 13 } = 63
\end{array}$$

Question 11

Evaluate the expression.
$$\left[ \begin{array} { c c } 
5 & - 1 \
4 & - 4
\end{array} \right] \left[ \begin{array} { c c } 
0 & 3 \
- 3 & 0
\end{array} \right] \left[ \begin{array} { c c } 
- 5 & 0 \
1 & 4
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } 0 & 60 \ - 48 & 48 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 0 & - 48 \ 60 & 48 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 0 & 0 \ - 12 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 15 & - 12 \ 60 & 12 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { c c } 0 & 60 \ - 48 & 48 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 0 & - 48 \ 60 & 48 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 0 & 0 \ - 12 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 15 & - 12 \ 60 & 12 \end{array} \right]$ 
E)  not possible

Question 12

Solve using any method.
$$\left\{ \begin{aligned}
7 x + 6 y & = 15 \
y & = x - 7
\end{aligned} \right.$$

Accepted Answer

A)  $( 7,0 )$ 
B)  $\left( - 6 , \frac { 51 } { 7 } \right)$ 
C)  $\left( - \frac { 27 } { 13 } , - \frac { 64 } { 13 } \right)$ 
D)  $\left( \frac { 57 } { 13 } , - \frac { 34 } { 13 } \right)$ 
E)  inconsistent 
A)  $( 7,0 )$ 
B)  $\left( - 6 , \frac { 51 } { 7 } \right)$ 
C)  $\left( - \frac { 27 } { 13 } , - \frac { 64 } { 13 } \right)$ 
D)  $\left( \frac { 57 } { 13 } , - \frac { 34 } { 13 } \right)$ 
E)  inconsistent

Question 13

Find the determinant of the matrix $\left[ \begin{array} { c c } - \frac { 1 } { 6 } & - \frac { 1 } { 2 } \ - 1 & - \frac { 4 } { 5 } \end{array} \right]$.

Accepted Answer

A)  $- \frac { 7 } { 30 }$ 
B)  $\frac { 19 } { 30 }$ 
C)  $\frac { 1 } { 24 }$ 
D)  $- \frac { 11 } { 30 }$ 
E)  $\frac { 7 } { 24 }$ 
A)  $- \frac { 7 } { 30 }$ 
B)  $\frac { 19 } { 30 }$ 
C)  $\frac { 1 } { 24 }$ 
D)  $- \frac { 11 } { 30 }$ 
E)  $\frac { 7 } { 24 }$

Question 14

Solve the system by the method of elimination.
$$\left\{ \begin{array} { l } 
7 x - 6 y = - 73 \
- 8 x - y = 52
\end{array} \right.$$

Accepted Answer

A)  $( 2 , - 68 )$ 
B)  $( - 7,4 )$ 
C)  $\left( \frac { 239 } { 15 } , \frac { 2812 } { 15 } \right)$ 
D)  $\left( - 8 , - \frac { 121 } { 7 } \right)$ 
E)  inconsistent 
A)  $( 2 , - 68 )$ 
B)  $( - 7,4 )$ 
C)  $\left( \frac { 239 } { 15 } , \frac { 2812 } { 15 } \right)$ 
D)  $\left( - 8 , - \frac { 121 } { 7 } \right)$ 
E)  inconsistent

Question 15

Write the partial fraction decomposition of the rational expression.
$\frac { 1 } { 100 x ^ { 2 } - 81 }$

Accepted Answer

A)  $\frac { 1 } { 18 } \left( \frac { x - 10 } { 10 x - 9 } - \frac { x - 10 } { 10 x + 9 } \right)$ 
B)  $\frac { 1 } { 100 x ^ { 2 } } - \frac { 1 } { 81 }$ 
C)  $\frac { 1 } { 18 } \left( \frac { 1 } { 10 x - 9 } - \frac { 1 } { 10 x + 9 } \right)$ 
D)  $\frac { 1 } { 9 } \left( \frac { 1 } { 10 x + 9 } - \frac { 1 } { 10 x - 9 } \right)$ 
E)  $\frac { 1 } { 9 } \left( \frac { 1 } { 10 x - 9 } - \frac { 1 } { 10 x + 9 } \right)$ 
A)  $\frac { 1 } { 18 } \left( \frac { x - 10 } { 10 x - 9 } - \frac { x - 10 } { 10 x + 9 } \right)$ 
B)  $\frac { 1 } { 100 x ^ { 2 } } - \frac { 1 } { 81 }$ 
C)  $\frac { 1 } { 18 } \left( \frac { 1 } { 10 x - 9 } - \frac { 1 } { 10 x + 9 } \right)$ 
D)  $\frac { 1 } { 9 } \left( \frac { 1 } { 10 x + 9 } - \frac { 1 } { 10 x - 9 } \right)$ 
E)  $\frac { 1 } { 9 } \left( \frac { 1 } { 10 x - 9 } - \frac { 1 } { 10 x + 9 } \right)$

Question 16

Find the inverse of the matrix $\left[ \begin{array} { c c } 8 & 16 \ - 24 & - 40 \end{array} \right]$.

Accepted Answer

A)  $\frac { 1 } { 7 } \left[ \begin{array} { c c } 8 & 16 \ - 24 & - 40 \end{array} \right]$ 
B)  $\frac { 1 } { 8 } \left[ \begin{array} { c c } - 5 & - 2 \ 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } - 8 & - 16 \ 40 & 24 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 8 & - 24 \ 32 & - 56 \end{array} \right]$ 
E)  $\frac { 1 } { 13 } \left[ \begin{array} { c c } - 8 & - 16 \ - 24 & 40 \end{array} \right]$ 
A)  $\frac { 1 } { 7 } \left[ \begin{array} { c c } 8 & 16 \ - 24 & - 40 \end{array} \right]$ 
B)  $\frac { 1 } { 8 } \left[ \begin{array} { c c } - 5 & - 2 \ 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } - 8 & - 16 \ 40 & 24 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 8 & - 24 \ 32 & - 56 \end{array} \right]$ 
E)  $\frac { 1 } { 13 } \left[ \begin{array} { c c } - 8 & - 16 \ - 24 & 40 \end{array} \right]$

Question 17

Write the augmented matrix for the system of linear equations.
$\left\{ \begin{array} { r } 
x - 8 y + 8 z = 9 \
8 y - 9 z = 1 \
x + z = 7
\end{array} \right.$

Accepted Answer

A)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 1 & 8 & - 9 & 1 \ 1 & 1 & 1 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 0 & 1 & 7 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ & 8 & - 9 & 1 \ 1 & & 1 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 8 & - 9 & 0 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$ 
A)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 1 & 8 & - 9 & 1 \ 1 & 1 & 1 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 0 & 1 & 7 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ & 8 & - 9 & 1 \ 1 & & 1 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 8 & - 9 & 0 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$

Question 18

Evaluate the expression.
$\frac { 2 } { 9 } \left[ \begin{array} { l l l } 
5 & - 2 & 1
\end{array} \right] + \left[ \begin{array} { l l l } 
4 & 8 & - 1
\end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { l l l } 9 & 6 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - \frac { 26 } { 9 } & - \frac { 76 } { 9 } & \frac { 11 } { 9 } \end{array} \right]$ 
C)  $\left[ \frac { 14 } { 9 } \quad \frac { 4 } { 9 } \quad \frac { 1 } { 9 } \right]$ 
D)  $\left[ \begin{array} { l l l } \frac { 46 } { 9 } & \frac { 68 } { 9 } & - \frac { 7 } { 9 } \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { l l l } 9 & 6 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - \frac { 26 } { 9 } & - \frac { 76 } { 9 } & \frac { 11 } { 9 } \end{array} \right]$ 
C)  $\left[ \frac { 14 } { 9 } \quad \frac { 4 } { 9 } \quad \frac { 1 } { 9 } \right]$ 
D)  $\left[ \begin{array} { l l l } \frac { 46 } { 9 } & \frac { 68 } { 9 } & - \frac { 7 } { 9 } \end{array} \right]$ 
E)  not possible

Question 19

Solve for $X$ in the equation given.
$9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 6 & - 5 & 3 \ 8 & - 3 & - 7 \end{array} \right]$ 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 20

Solve the system by the method of elimination.
$$\left\{ \begin{array} { c } 
5 x - y = 11 \
- 7 x - y = - 25
\end{array} \right.$$

Accepted Answer

A)  $( 1,18 )$ 
B)  $( 3,4 )$ 
C)  $\left( - \frac { 7 } { 6 } , - \frac { 157 } { 6 } \right)$ 
D)  $\left( - 5 , \frac { 6 } { 5 } \right)$ 
E)  inconsistent 
A)  $( 1,18 )$ 
B)  $( 3,4 )$ 
C)  $\left( - \frac { 7 } { 6 } , - \frac { 157 } { 6 } \right)$ 
D)  $\left( - 5 , \frac { 6 } { 5 } \right)$ 
E)  inconsistent

Solve the system of linear equations. $\left\{ \begin{aligned}2 x - 2 y + 3 z & = - 21 \\2 x + z & = - 11 \\- 2 x + 4 y - 4 z & = 28\end{aligned} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 5 } { x ^ { 2 } + 10 x + 16 }$

Identify the elementary row operation being performed to obtain the new rowequivalent matrix. Original Matrix New Row-Equivalent Matrix 7 6 6 1 4 -6 12 26 -24 1 4 -6

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

An object moving vertically is at the given heights at the specified times. Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { o } t + s _ { o }$ for the object. At $t = 1$ second, $s = 198$ feet At $t = 2$ seconds, $s = 182$ feet At $t = 3$ seconds, $s = 134$ feet

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{array} { l } 7 x - 3 y - 9 z = 22 \\2 x + y + 3 z = - 3 \\2 x - 7 y - 3 z = - 17\end{array} \right.$

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

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

Solve the system by the method of substitution. $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 625 \\7 x - 24 y & = 0\end{aligned} \right.$

Find the minor $M _ { 13 }$ and its cofactor $C _ { 13 }$ of the matrix $\left[ \begin{array} { c c c } - 9 & 6 & - 24 \\ 9 & - 6 & 18 \\ - 3 & 9 & - 18 \end{array} \right]$

Evaluate the expression. $\left[ \begin{array} { c c } 5 & - 1 \\4 & - 4\end{array} \right] \left[ \begin{array} { c c } 0 & 3 \\- 3 & 0\end{array} \right] \left[ \begin{array} { c c } - 5 & 0 \\1 & 4\end{array} \right]$

Solve using any method. $\left\{ \begin{aligned}7 x + 6 y & = 15 \\y & = x - 7\end{aligned} \right.$

Find the determinant of the matrix $\left[ \begin{array} { c c } - \frac { 1 } { 6 } & - \frac { 1 } { 2 } \\ - 1 & - \frac { 4 } { 5 } \end{array} \right]$ .

Solve the system by the method of elimination. $\left\{ \begin{array} { l } 7 x - 6 y = - 73 \\- 8 x - y = 52\end{array} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { 100 x ^ { 2 } - 81 }$

Find the inverse of the matrix $\left[ \begin{array} { c c } 8 & 16 \\ - 24 & - 40 \end{array} \right]$ .

Write the augmented matrix for the system of linear equations. $\left\{ \begin{array} { r } x - 8 y + 8 z = 9 \\8 y - 9 z = 1 \\x + z = 7\end{array} \right.$

Evaluate the expression. $\frac { 2 } { 9 } \left[ \begin{array} { l l l } 5 & - 2 & 1\end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1\end{array} \right]$

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

Solve the system by the method of elimination. $\left\{ \begin{array} { c } 5 x - y = 11 \\- 7 x - y = - 25\end{array} \right.$

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Exam 7: Linear Systems and Matrices

Solve the system of linear equations. {2x−2y+3z=−212x+z=−11−2x+4y−4z=28\left\{ \begin{aligned}2 x - 2 y + 3 z & = - 21 \\2 x + z & = - 11 \\- 2 x + 4 y - 4 z & = 28\end{aligned} \right.⎩⎨⎧​2x−2y+3z2x+z−2x+4y−4z​=−21=−11=28​

Write the partial fraction decomposition of the rational expression. 5x2+10x+16\frac { 5 } { x ^ { 2 } + 10 x + 16 }x2+10x+165​

Identify the elementary row operation being performed to obtain the new rowequivalent matrix. Original Matrix New Row-Equivalent Matrix 7 6 6 1 4 -6 12 26 -24 1 4 -6

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​])

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{aligned}5.2 x + 8.1 y & = 6.9 \\- 2.6 x + 1.1 y & = - 0.7\end{aligned} \right.{5.2x+8.1y−2.6x+1.1y​=6.9=−0.7​

Solve the system by the method of substitution. {x2+y2=6257x−24y=0\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 625 \\7 x - 24 y & = 0\end{aligned} \right.{x2+y27x−24y​=625=0​

Find the minor M13M _ { 13 }M13​ and its cofactor C13C _ { 13 }C13​ of the matrix [−96−249−618−39−18]\left[ \begin{array} { c c c } - 9 & 6 & - 24 \\ 9 & - 6 & 18 \\ - 3 & 9 & - 18 \end{array} \right]​−99−3​6−69​−2418−18​​

Evaluate the expression. [5−14−4][03−30][−5014]\left[ \begin{array} { c c } 5 & - 1 \\4 & - 4\end{array} \right] \left[ \begin{array} { c c } 0 & 3 \\- 3 & 0\end{array} \right] \left[ \begin{array} { c c } - 5 & 0 \\1 & 4\end{array} \right][54​−1−4​][0−3​30​][−51​04​]

Solve using any method. {7x+6y=15y=x−7\left\{ \begin{aligned}7 x + 6 y & = 15 \\y & = x - 7\end{aligned} \right.{7x+6yy​=15=x−7​

Find the determinant of the matrix [−16−12−1−45]\left[ \begin{array} { c c } - \frac { 1 } { 6 } & - \frac { 1 } { 2 } \\ - 1 & - \frac { 4 } { 5 } \end{array} \right][−61​−1​−21​−54​​] .

Solve the system by the method of elimination. {7x−6y=−73−8x−y=52\left\{ \begin{array} { l } 7 x - 6 y = - 73 \\- 8 x - y = 52\end{array} \right.{7x−6y=−73−8x−y=52​

Write the partial fraction decomposition of the rational expression. 1100x2−81\frac { 1 } { 100 x ^ { 2 } - 81 }100x2−811​

Find the inverse of the matrix [816−24−40]\left[ \begin{array} { c c } 8 & 16 \\ - 24 & - 40 \end{array} \right][8−24​16−40​] .

Write the augmented matrix for the system of linear equations. {x−8y+8z=98y−9z=1x+z=7\left\{ \begin{array} { r } x - 8 y + 8 z = 9 \\8 y - 9 z = 1 \\x + z = 7\end{array} \right.⎩⎨⎧​x−8y+8z=98y−9z=1x+z=7​

Evaluate the expression. 29[5−21]+[48−1]\frac { 2 } { 9 } \left[ \begin{array} { l l l } 5 & - 2 & 1\end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1\end{array} \right]92​[5​−2​1​]+[4​8​−1​]

Solve the system by the method of elimination. {5x−y=11−7x−y=−25\left\{ \begin{array} { c } 5 x - y = 11 \\- 7 x - y = - 25\end{array} \right.{5x−y=11−7x−y=−25​