Question 1

Determine whether the system of linear equations is consistent or inconsistent.
$$\left\{ \begin{aligned}
- x + 9 y & = 5 \
- 4 x + 36 y & = 21
\end{aligned} \right.$$

Accepted Answer

A)  inconsistent 
B)  consistent 
A)  inconsistent 
B)  consistent

Question 2

Solve the system of equations.
$$\left\{ \begin{array} { c } 
- \frac { 1 } { x } - \frac { 4 } { y } - \frac { 1 } { z } = - 3 \
- \frac { 5 } { x } - \frac { 2 } { y } - \frac { 2 } { z } = - 5 \
- \frac { 1 } { x } - \frac { 5 } { y } + \frac { 2 } { z } = - 3
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 41 } { 57 } , \frac { 10 } { 19 } , \frac { 10 } { 57 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 1 } { 5 } , - \frac { 1 } { 19 } \right)$ 
C)  $\left( \frac { 827 } { 285 } , \frac { 13 } { 10 } , \frac { 10 } { 57 } \right)$ 
D)  $\left( \frac { 85 } { 41 } , \frac { 17 } { 6 } , \frac { 17 } { 2 } \right)$ 
E)  $\left( \frac { 57 } { 41 } , \frac { 19 } { 10 } , \frac { 57 } { 10 } \right)$ 
A)  $\left( \frac { 41 } { 57 } , \frac { 10 } { 19 } , \frac { 10 } { 57 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 1 } { 5 } , - \frac { 1 } { 19 } \right)$ 
C)  $\left( \frac { 827 } { 285 } , \frac { 13 } { 10 } , \frac { 10 } { 57 } \right)$ 
D)  $\left( \frac { 85 } { 41 } , \frac { 17 } { 6 } , \frac { 17 } { 2 } \right)$ 
E)  $\left( \frac { 57 } { 41 } , \frac { 19 } { 10 } , \frac { 57 } { 10 } \right)$

Question 3

Write the system of linear equations as a matrix equation $A X = B$, and use Gauss-Jordan elimination on the augmented matrix $[ A \vdots B ]$ to solve for the matrix $X$.
$$\left\{ \begin{aligned}
x _ { 1 } + 6 x _ { 2 } + 9 x _ { 3 } & = - 44 \
- 7 x _ { 1 } + 2 x _ { 2 } - x _ { 3 } & = - 54 \
8 x _ { 1 } + 3 x _ { 2 } + 6 x _ { 3 } & = 26
\end{aligned} \right.$$

Accepted Answer

A)  $X = \left[ \begin{array} { l } 28 \ 12 \ 21 \end{array} \right]$ 
B)  $X = \left[ \begin{array} { c } 12 \ - 7 \ - 4 \end{array} \right]$ 
C)  $X = \left[ \begin{array} { c } 7 \ - 4 \ - 3 \end{array} \right]$ 
D)  $X = \left[ \begin{array} { l } - 12 \ - 28 \ - 21 \end{array} \right]$ 
E)  $X = \left[ \begin{array} { c } - 7 \ 3 \ - 4 \end{array} \right]$ 
A)  $X = \left[ \begin{array} { l } 28 \ 12 \ 21 \end{array} \right]$ 
B)  $X = \left[ \begin{array} { c } 12 \ - 7 \ - 4 \end{array} \right]$ 
C)  $X = \left[ \begin{array} { c } 7 \ - 4 \ - 3 \end{array} \right]$ 
D)  $X = \left[ \begin{array} { l } - 12 \ - 28 \ - 21 \end{array} \right]$ 
E)  $X = \left[ \begin{array} { c } - 7 \ 3 \ - 4 \end{array} \right]$

Question 4

Solve the system of linear equations.
$$\left\{ \begin{aligned}
x + y + z + w & = 11 \
- 2 x - y - 3 z + 4 w & = - 5 \
- 2 x - 5 z - w & = - 23 \
3 x + 5 y + z - 2 w & = 16
\end{aligned} \right.$$

Accepted Answer

A)  $( 5,1,3,2 )$ 
B)  $( 5,2,1,3 )$ 
C)  $( 3,1,2,5 )$ 
D)  $( 5,1,2,3 )$ 
E)  inconsistent 
A)  $( 5,1,3,2 )$ 
B)  $( 5,2,1,3 )$ 
C)  $( 3,1,2,5 )$ 
D)  $( 5,1,2,3 )$ 
E)  inconsistent

Question 5

Given:
$$A = \left[ \begin{array} { r r r } 
4 & 2 & - 3 \
1 & - 2 & 2
\end{array} \right] , B = \left[ \begin{array} { r r r } 
0 & - 2 & 5 \
5 & 4 & 2
\end{array} \right] , C = \left[ \begin{array} { r r } 
- 4 & 1 \
- 5 & - 1 \
- 3 & - 3
\end{array} \right] ,$$
determine $C A - C B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 20 & - 22 & 32 \ - 16 & - 14 & 40 \ 0 & 6 & 24 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 16 & - 20 & 24 \ - 4 & 6 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } - 12 & 24 \ 46 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 16 & - 4 \ - 20 & 6 \ 24 & 0 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { r r r } - 20 & - 22 & 32 \ - 16 & - 14 & 40 \ 0 & 6 & 24 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 16 & - 20 & 24 \ - 4 & 6 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } - 12 & 24 \ 46 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 16 & - 4 \ - 20 & 6 \ 24 & 0 \end{array} \right]$ 
E)  not possible

Question 6

Find a system of linear equations that has the following solution.
$\left( - \frac { 4 } { 7 } , 10 \right)$

Accepted Answer

A) 
$\left\{ \begin{array} { l } 28 x + 15 y = \frac { 1900 } { 7 } \ 56 x + 10 y = \frac { 3880 } { 7 } \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 28 y + 15 x = 134 \ 56 y + 10 x = 68 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 56 x + 10 y = - 166 \ 28 x + 15 y = - 132 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 28 y + 15 x = \frac { 1900 } { 7 } \ 56 y + 10 x = \frac { 3880 } { 7 } \end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 28 x + 15 y = 134 \ 56 x + 10 y = 68 \end{array} \right.$ 
A) 
$\left\{ \begin{array} { l } 28 x + 15 y = \frac { 1900 } { 7 } \ 56 x + 10 y = \frac { 3880 } { 7 } \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 28 y + 15 x = 134 \ 56 y + 10 x = 68 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 56 x + 10 y = - 166 \ 28 x + 15 y = - 132 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 28 y + 15 x = \frac { 1900 } { 7 } \ 56 y + 10 x = \frac { 3880 } { 7 } \end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 28 x + 15 y = 134 \ 56 x + 10 y = 68 \end{array} \right.$

Question 7

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)  $\left\{\begin{aligned}
-4 x-9 w &=-9 \
7 x-8 y &=1 \
-4 y-7 z-9 w &=-8 \
-4 y+z &=-8
\end{aligned}\right.$ 
E)    
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)  $\left\{\begin{aligned}
-4 x-9 w &=-9 \
7 x-8 y &=1 \
-4 y-7 z-9 w &=-8 \
-4 y+z &=-8
\end{aligned}\right.$ 
E)

Question 8

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

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 9

Solve the system by the method of elimination.
$$\left\{ \begin{array} { c } 
\frac { 1 } { 9 } x - \frac { 1 } { 8 } y = 6 \
- 48 x + 54 y = - 2591
\end{array} \right.$$

Accepted Answer

A)  $( 9 , - 40 )$ 
B)  no solution 
C)  $\left( \frac { 2915 } { 102 } , - \frac { 2303 } { 102 } \right)$ 
D)  $\left( \frac { 5183 } { 96 } , \frac { 1 } { 108 } \right)$ 
E)  infinitely many solutions 
A)  $( 9 , - 40 )$ 
B)  no solution 
C)  $\left( \frac { 2915 } { 102 } , - \frac { 2303 } { 102 } \right)$ 
D)  $\left( \frac { 5183 } { 96 } , \frac { 1 } { 108 } \right)$ 
E)  infinitely many solutions

Question 10

Solve for $x$ given the following equation involving a determinant.
$\left| \begin{array} { c c } 
x + 1 & 7 \
- 1 & x + 9
\end{array} \right| = 0$

Accepted Answer

A)  $x = 8,2$ 
B)  $x = - 9 , - 1$ 
C)  $x = 9,1$ 
D)  $x = - 8 , - 2$ 
E)  $x = 8 , - 7$ 
A)  $x = 8,2$ 
B)  $x = - 9 , - 1$ 
C)  $x = 9,1$ 
D)  $x = - 8 , - 2$ 
E)  $x = 8 , - 7$

Question 11

Solve the system of equations below using Gaussian elimination.
$$\begin{aligned}
5 x + 4 y + 3 z & = 90 \
x - 2 y + 2 z & = 60 \
x - y - z & = - 30
\end{aligned}$$

Accepted Answer

A)  $( 1 , - 1,32 )$ 
B)  $( 1,0,31 )$ 
C)  $( 0,1,29 )$ 
D)  $( - 1,1,28 )$ 
E)  $( 0,0,30 )$ 
A)  $( 1 , - 1,32 )$ 
B)  $( 1,0,31 )$ 
C)  $( 0,1,29 )$ 
D)  $( - 1,1,28 )$ 
E)  $( 0,0,30 )$

Question 12

Solve the system by the method of elimination.
$$\left\{ \begin{array} { c } 
4 x + 5 y = - 71 \
x - y = - 2
\end{array} \right.$$

Accepted Answer

A)  $( - 6 , - 4 )$ 
B)  $( - 9 , - 7 )$ 
C)  $\left( - \frac { 61 } { 3 } , \frac { 52 } { 3 } \right)$ 
D)  $\left( 8 , - \frac { 111 } { 4 } \right)$ 
E)  inconsistent 
A)  $( - 6 , - 4 )$ 
B)  $( - 9 , - 7 )$ 
C)  $\left( - \frac { 61 } { 3 } , \frac { 52 } { 3 } \right)$ 
D)  $\left( 8 , - \frac { 111 } { 4 } \right)$ 
E)  inconsistent

Question 13

Find a solution of the system of equations and verify your result using matrix multiplication.
$\left\{ \begin{array} { r } 
- 8 x + 3 y = 20 \
3 x - 5 y = - 9
\end{array} \right.$

Accepted Answer

A)  $\left[ \begin{array} { r } - \frac { 3 } { 8 } \ \frac { 17 } { 3 } \end{array} \right]$ 
B)  $\left[ \begin{array} { r } - \frac { 65 } { 38 } \ \frac { 40 } { 19 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r } - \frac { 73 } { 49 } \ \frac { 132 } { 49 } \end{array} \right]$ 
D)  $\left[ \begin{array} { r } - \frac { 73 } { 31 } \ \frac { 12 } { 31 } \end{array} \right]$ 
E)  $\left[ \begin{array} { r } - \frac { 31 } { 73 } \ \frac { 31 } { 12 } \end{array} \right]$ 
A)  $\left[ \begin{array} { r } - \frac { 3 } { 8 } \ \frac { 17 } { 3 } \end{array} \right]$ 
B)  $\left[ \begin{array} { r } - \frac { 65 } { 38 } \ \frac { 40 } { 19 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r } - \frac { 73 } { 49 } \ \frac { 132 } { 49 } \end{array} \right]$ 
D)  $\left[ \begin{array} { r } - \frac { 73 } { 31 } \ \frac { 12 } { 31 } \end{array} \right]$ 
E)  $\left[ \begin{array} { r } - \frac { 31 } { 73 } \ \frac { 31 } { 12 } \end{array} \right]$

Question 14

Perform the indicated row operations on the matrix. Show the final result.
$$\left[ \begin{array} { c c c } 
1 & - 1 & 9 \
- 3 & 4 & 4 \
6 & - 8 & - 8
\end{array} \right]$$
Add 3 times $R _ { 1 }$ to $R _ { 2 }$.
Add $- 6$ times $R _ { 1 }$ to $R _ { 3 }$.

Accepted Answer

A)  $\left[ \begin{array} { c c c } 6 & - 14 & - 224 \ - 3 & 4 & 4 \ 6 & - 8 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ 0 & 1 & 13 \ 0 & - 9 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ 0 & 1 & 31 \ 0 & - 2 & - 62 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ - 8 & 11 & 21 \ - 35 & 47 & 57 \end{array} \right]$
Е) $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ 0 & 10 & - 50 \ 0 & - 11 & - 11 \end{array} \right]$ 
A)  $\left[ \begin{array} { c c c } 6 & - 14 & - 224 \ - 3 & 4 & 4 \ 6 & - 8 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ 0 & 1 & 13 \ 0 & - 9 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ 0 & 1 & 31 \ 0 & - 2 & - 62 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ - 8 & 11 & 21 \ - 35 & 47 & 57 \end{array} \right]$
Е) $\left[ \begin{array} { c c c } 1 & - 1 & 9 \ 0 & 10 & - 50 \ 0 & - 11 & - 11 \end{array} \right]$

Question 15

Solve the system by the method of elimination.
$$\left\{ \begin{aligned}
\frac { x + 7 } { 5 } + \frac { y - 2 } { 5 } & = - 2 \
x - y & = - 14
\end{aligned} \right.$$

Accepted Answer

A)  $\left( - \frac { 29 } { 2 } , - \frac { 1 } { 2 } \right)$ 
B)  $\left( - \frac { 1 } { 2 } , - \frac { 29 } { 2 } \right)$ 
C)  $\left( - \frac { 2 } { 29 } , - \frac { 2 } { 1 } \right)$ 
D)  $( - 29 , - 15 )$ 
E)  no solution 
A)  $\left( - \frac { 29 } { 2 } , - \frac { 1 } { 2 } \right)$ 
B)  $\left( - \frac { 1 } { 2 } , - \frac { 29 } { 2 } \right)$ 
C)  $\left( - \frac { 2 } { 29 } , - \frac { 2 } { 1 } \right)$ 
D)  $( - 29 , - 15 )$ 
E)  no solution

Question 16

Find the inverse of the matrix $\left[ \begin{array} { c c } 6 & 12 \ - 18 & - 30 \end{array} \right]$.

Accepted Answer

A)  $\frac { 1 } { 7 } \left[ \begin{array} { c c } 6 & 12 \ - 18 & - 30 \end{array} \right]$ 
B)  $\frac { 1 } { 6 } \left[ \begin{array} { c c } - 5 & - 2 \ 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } - 6 & - 12 \ 30 & 18 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 6 & - 18 \ 24 & - 42 \end{array} \right]$ 
E)  $\frac { 1 } { 13 } \left[ \begin{array} { c c } - 6 & - 12 \ - 18 & 30 \end{array} \right]$ 
A)  $\frac { 1 } { 7 } \left[ \begin{array} { c c } 6 & 12 \ - 18 & - 30 \end{array} \right]$ 
B)  $\frac { 1 } { 6 } \left[ \begin{array} { c c } - 5 & - 2 \ 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } - 6 & - 12 \ 30 & 18 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 6 & - 18 \ 24 & - 42 \end{array} \right]$ 
E)  $\frac { 1 } { 13 } \left[ \begin{array} { c c } - 6 & - 12 \ - 18 & 30 \end{array} \right]$

Question 17

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

Write the partial fraction decomposition of the improper rational expression.
$$\frac { x ^ { 3 } - 4 x ^ { 2 } + 3 x + 2 } { x ^ { 2 } + x - 2 }$$

Accepted Answer

A)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } + \frac { 28 } { x + 2 } \right)$ 
B)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 18 } { x - 1 } + \frac { 28 } { x + 2 } \right)$ 
C)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 18 } { x + 1 } + \frac { 28 } { x - 2 } \right)$ 
D)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } - \frac { 28 } { x + 2 } \right)$ 
E)  $\frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } + \frac { 28 } { x + 2 } \right)$ 
A)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } + \frac { 28 } { x + 2 } \right)$ 
B)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 18 } { x - 1 } + \frac { 28 } { x + 2 } \right)$ 
C)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 18 } { x + 1 } + \frac { 28 } { x - 2 } \right)$ 
D)  $x - 5 + \frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } - \frac { 28 } { x + 2 } \right)$ 
E)  $\frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } + \frac { 28 } { x + 2 } \right)$

Question 19

Use a system of equations to find the specified equation that passes through the points. Solve the system using matrices.
Parabola: $y = a x ^ { 2 } + b x + c$

Accepted Answer

A)  $y = x ^ { 2 } - 3 x + 4$ 
B)  $y = - x ^ { 2 } - 3 x + 1$ 
C)  $y = - x ^ { 2 } + 3 x + 4$ 
D)  $y = - x ^ { 2 } + 3 x + 1$ 
E)  $y = - x ^ { 2 } - 2 x + 1$ 
A)  $y = x ^ { 2 } - 3 x + 4$ 
B)  $y = - x ^ { 2 } - 3 x + 1$ 
C)  $y = - x ^ { 2 } + 3 x + 4$ 
D)  $y = - x ^ { 2 } + 3 x + 1$ 
E)  $y = - x ^ { 2 } - 2 x + 1$

Question 20

Write the augmented matrix for the system of linear equations.
$$\left\{ \begin{aligned}
x + 4 y - z & = - 9 \
- 9 y + 4 z & = - 6 \
x + 5 z & = - 4
\end{aligned} \right.$$

Accepted Answer

A) 
$\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ 1 & - 9 & 4 & - 6 \ 1 & 1 & 5 & - 4 \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ 0 & - 9 & 4 & - 6 \ 1 & 0 & 5 & - 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ & - 9 & 4 & - 6 \ 1 & & 5 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ - 9 & 4 & 0 & - 6 \ 1 & 5 & 0 & - 4 \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ 0 & - 9 & 4 & - 6 \ 1 & 5 & 0 & - 4 \end{array} \right]$ 
A) 
$\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ 1 & - 9 & 4 & - 6 \ 1 & 1 & 5 & - 4 \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ 0 & - 9 & 4 & - 6 \ 1 & 0 & 5 & - 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ & - 9 & 4 & - 6 \ 1 & & 5 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ - 9 & 4 & 0 & - 6 \ 1 & 5 & 0 & - 4 \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c : c } 1 & 4 & - 1 & - 9 \ 0 & - 9 & 4 & - 6 \ 1 & 5 & 0 & - 4 \end{array} \right]$

Determine whether the system of linear equations is consistent or inconsistent. $\left\{ \begin{aligned}- x + 9 y & = 5 \\- 4 x + 36 y & = 21\end{aligned} \right.$

Solve the system of equations. $\left\{ \begin{array} { c } - \frac { 1 } { x } - \frac { 4 } { y } - \frac { 1 } { z } = - 3 \\- \frac { 5 } { x } - \frac { 2 } { y } - \frac { 2 } { z } = - 5 \\- \frac { 1 } { x } - \frac { 5 } { y } + \frac { 2 } { z } = - 3\end{array} \right.$

Solve the system of linear equations. $\left\{ \begin{aligned}x + y + z + w & = 11 \\- 2 x - y - 3 z + 4 w & = - 5 \\- 2 x - 5 z - w & = - 23 \\3 x + 5 y + z - 2 w & = 16\end{aligned} \right.$

Given: $A = \left[ \begin{array} { r r r } 4 & 2 & - 3 \\1 & - 2 & 2\end{array} \right] , B = \left[ \begin{array} { r r r } 0 & - 2 & 5 \\5 & 4 & 2\end{array} \right] , C = \left[ \begin{array} { r r } - 4 & 1 \\- 5 & - 1 \\- 3 & - 3\end{array} \right] ,$ determine $C A - C B$ .

Find a system of linear equations that has the following solution. $\left( - \frac { 4 } { 7 } , 10 \right)$

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

Solve the system by the method of elimination. $\left\{ \begin{array} { c } \frac { 1 } { 9 } x - \frac { 1 } { 8 } y = 6 \\- 48 x + 54 y = - 2591\end{array} \right.$

Solve for $x$ given the following equation involving a determinant. $\left| \begin{array} { c c } x + 1 & 7 \\- 1 & x + 9\end{array} \right| = 0$

Solve the system of equations below using Gaussian elimination. 5x+4y+3z =90 x-2y+2z =60 x-y-z =-30

Solve the system by the method of elimination. $\left\{ \begin{array} { c } 4 x + 5 y = - 71 \\x - y = - 2\end{array} \right.$

Find a solution of the system of equations and verify your result using matrix multiplication. $\left\{ \begin{array} { r } - 8 x + 3 y = 20 \\3 x - 5 y = - 9\end{array} \right.$

Perform the indicated row operations on the matrix. Show the final result. $\left[ \begin{array} { c c c } 1 & - 1 & 9 \\- 3 & 4 & 4 \\6 & - 8 & - 8\end{array} \right]$ Add 3 times $R _ { 1 }$ to $R _ { 2 }$ . Add $- 6$ times $R _ { 1 }$ to $R _ { 3 }$ .

Solve the system by the method of elimination. $\left\{ \begin{aligned}\frac { x + 7 } { 5 } + \frac { y - 2 } { 5 } & = - 2 \\x - y & = - 14\end{aligned} \right.$

Find the inverse of the matrix $\left[ \begin{array} { c c } 6 & 12 \\ - 18 & - 30 \end{array} \right]$ .

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

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 3 } - 4 x ^ { 2 } + 3 x + 2 } { x ^ { 2 } + x - 2 }$

Write the augmented matrix for the system of linear equations. $\left\{ \begin{aligned}x + 4 y - z & = - 9 \\- 9 y + 4 z & = - 6 \\x + 5 z & = - 4\end{aligned} \right.$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Exam 7: Linear Systems and Matrices

Determine whether the system of linear equations is consistent or inconsistent. {−x+9y=5−4x+36y=21\left\{ \begin{aligned}- x + 9 y & = 5 \\- 4 x + 36 y & = 21\end{aligned} \right.{−x+9y−4x+36y​=5=21​

Find a system of linear equations that has the following solution. (−47,10)\left( - \frac { 4 } { 7 } , 10 \right)(−74​,10)

Solve the system by the method of elimination. {19x−18y=6−48x+54y=−2591\left\{ \begin{array} { c } \frac { 1 } { 9 } x - \frac { 1 } { 8 } y = 6 \\- 48 x + 54 y = - 2591\end{array} \right.{91​x−81​y=6−48x+54y=−2591​

Solve for xxx given the following equation involving a determinant. ∣x+17−1x+9∣=0\left| \begin{array} { c c } x + 1 & 7 \\- 1 & x + 9\end{array} \right| = 0​x+1−1​7x+9​​=0