Question 1

Find the inverse of the matrix. 
 $\left[ \begin{array} { l l l } 
1 & 5 & 2 \
0 & 1 & 5 \
0 & 0 & 1
\end{array} \right]$

Accepted Answer

A)   $\left[ \begin{array} { c c c } 
1 & 5 & - 23 \
0 & 1 & 5 \
0 & 0 & 1
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c c } 
- 1 & - 5 & 23 \
0 & - 1 & - 5 \
0 & 0 & - 1
\end{array} \right]$ 
C)   $\left[ \begin{array} { c c c } 
1 & - 5 & - 23 \
0 & 1 & - 5 \
0 & 0 & 1
\end{array} \right]$ 
D)   $\left[ \begin{array} { l l l } 
1 & 5 & 23 \
0 & 1 & 5 \
0 & 0 & 1
\end{array} \right]$ 
E)   $\left[ \begin{array} { c c c } 
1 & - 5 & 23 \
0 & 1 & - 5 \
0 & 0 & 1
\end{array} \right]$ 
A)   $\left[ \begin{array} { c c c } 
1 & 5 & - 23 \
0 & 1 & 5 \
0 & 0 & 1
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c c } 
- 1 & - 5 & 23 \
0 & - 1 & - 5 \
0 & 0 & - 1
\end{array} \right]$ 
C)   $\left[ \begin{array} { c c c } 
1 & - 5 & - 23 \
0 & 1 & - 5 \
0 & 0 & 1
\end{array} \right]$ 
D)   $\left[ \begin{array} { l l l } 
1 & 5 & 23 \
0 & 1 & 5 \
0 & 0 & 1
\end{array} \right]$ 
E)   $\left[ \begin{array} { c c c } 
1 & - 5 & 23 \
0 & 1 & - 5 \
0 & 0 & 1
\end{array} \right]$

Question 2

Write the system of linear equations as a matrix equation, AX = B.   $$\left\{ \begin{aligned}
x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } & = 18 \
- x _ { 1 } + 3 x _ { 2 } - x _ { 3 } & = 18 \
3 x _ { 1 } - 3 x _ { 2 } + 3 x _ { 3 } & = 18
\end{aligned} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } 
1 & 3 & 2 \
1 & 3 & 1 \
3 & 3 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 
1 & - 3 & 2 \
- 1 & 3 & - 1 \
3 & - 3 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
- 18 \
- 18 \
- 18
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 
1 & - 3 & 2 \
- 1 & 3 & - 1 \
3 & - 3 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
1 & - 1 & 3 \
- 3 & 3 & 3 \
2 & - 1 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c c } 
1 & - 3 & 2 \
- 1 & 3 & - 1 \
3 & - 3 & 3
\end{array} \right] \left[ \begin{array} { c } 
- x _ { 1 } \
- x _ { 2 } \
- x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$ 
A)  $\left[ \begin{array} { l l l } 
1 & 3 & 2 \
1 & 3 & 1 \
3 & 3 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 
1 & - 3 & 2 \
- 1 & 3 & - 1 \
3 & - 3 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
- 18 \
- 18 \
- 18
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 
1 & - 3 & 2 \
- 1 & 3 & - 1 \
3 & - 3 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
1 & - 1 & 3 \
- 3 & 3 & 3 \
2 & - 1 & 3
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c c } 
1 & - 3 & 2 \
- 1 & 3 & - 1 \
3 & - 3 & 3
\end{array} \right] \left[ \begin{array} { c } 
- x _ { 1 } \
- x _ { 2 } \
- x _ { 3 }
\end{array} \right] = \left[ \begin{array} { l } 
18 \
18 \
18
\end{array} \right]$

Question 3

Use the matrix capabilities of a graphing utility to find the determinant of the matrix $\left[ \begin{array} { c c c } 
16 & 24 & 8 \
0 & 40 & - 16 \
0 & 0 & - 16
\end{array} \right]$ .

Accepted Answer

A) -1,024 
B) 0 
C)  $- 10,240$ 
D) -2,560 
E)  $15,360$ 
A) -1,024 
B) 0 
C)  $- 10,240$ 
D) -2,560 
E)  $15,360$

Question 4

Find the determinant of the matrix.   $\left[ \begin{array} { c c } 
2 & - 2 \
8 & - 16
\end{array} \right]$

Accepted Answer

A)  $- \frac { 1 } { 16 }$ 
B)  $\frac { 1 } { 16 }$ 
C) 0 
D) 16 
E)  $- 16$ 
A)  $- \frac { 1 } { 16 }$ 
B)  $\frac { 1 } { 16 }$ 
C) 0 
D) 16 
E)  $- 16$

Question 5

Use Cramer's rule to find the solution of the system, if possible.   $$\left\{ \begin{aligned}
5 x - y & = 12 \
x + y & = 0
\end{aligned} \right.$$

Accepted Answer

A) x = 2, y = -2 
B) x = 5, y = -12 
C) x = 5, y = -5 
D) The system is inconsistent. 
E) The equations are dependent. 
A) x = 2, y = -2 
B) x = 5, y = -12 
C) x = 5, y = -5 
D) The system is inconsistent. 
E) The equations are dependent.

Question 6

A hair product company sells three types of hair products for $30, $20 and $10 per unit.In one year, the total revenue for the three products was $820,000 which corresponded to the sale of 42,000 units.The company sold half as many units of the $30 products as units of the $20 product.Use Cramer's Rule to solve a system of linear equations to find how many units of each product were sold. ​

Accepted Answer

A) 10,000 units at $30, 20,000 units at $20, 12,000 units at $10. 
B) 10,000 units at $30, 20,000 units at $20, 18,000 units at $10. 
C) 10,000 units at $30, 20,000 units at $20, 20,000 units at $10. 
D) 10,000 units at $30, 20,000 units at $20, 14,000 units at $10. 
E) 10,000 units at $30, 20,000 units at $20, 16,000 units at $10. 
A) 10,000 units at $30, 20,000 units at $20, 12,000 units at $10. 
B) 10,000 units at $30, 20,000 units at $20, 18,000 units at $10. 
C) 10,000 units at $30, 20,000 units at $20, 20,000 units at $10. 
D) 10,000 units at $30, 20,000 units at $20, 14,000 units at $10. 
E) 10,000 units at $30, 20,000 units at $20, 16,000 units at $10.

Question 7

Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r r } 
5 & - 7 & - 3 & 6 \
- 6 & - 6 & 2 & - 44 \
2 & - 4 & - 2 & - 4
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 6 \
0 & 1 & 0 & 3 \
0 & 0 & 1 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 1 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & 1
\end{array} \right]$ 
C)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 7 \
0 & 1 & 0 & 2 \
0 & 0 & 1 & 5
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 0 \
0 & 1 & 0 & 0 \
0 & 0 & 1 & 0
\end{array} \right]$ 
E)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 7 \
0 & 1 & 0 & 5 \
0 & 0 & 1 & 2
\end{array} \right]$ 
A)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 6 \
0 & 1 & 0 & 3 \
0 & 0 & 1 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 1 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & 1
\end{array} \right]$ 
C)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 7 \
0 & 1 & 0 & 2 \
0 & 0 & 1 & 5
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 0 \
0 & 1 & 0 & 0 \
0 & 0 & 1 & 0
\end{array} \right]$ 
E)  $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 7 \
0 & 1 & 0 & 5 \
0 & 0 & 1 & 2
\end{array} \right]$

Question 8

Determine whether the matrix is in row-echelon form.If it is, determine if it is also in reduced row-echelon form. $$\left[ \begin{array} { r r r r } 
1 & 9 & - 9 & - 6 \
0 & 1 & 0 & - 2 \
0 & 0 & 1 & 1
\end{array} \right]$$

Accepted Answer

A) row-echelon form 
B) row-echelon form and reduced row-echelon form 
C) neither 
A) row-echelon form 
B) row-echelon form and reduced row-echelon form 
C) neither

Question 9

Evaluate the determinant $\mid \begin{array} { c c } 
e ^ { 7 x } & e ^ { 4 x } \
7 e ^ { 7 x } & 4 e ^ { 4 x }
\end{array}$ in which the entries are functions.

Accepted Answer

A)  $- 3 e ^ { 11 x }$ 
B)  $\frac { 7 } { 4 } e ^ { 28 x }$ 
C)  $\frac { 4 } { 7 } e ^ { 11 x }$ 
D)  $- 3 e ^ { 28 x }$ 
E)  $- \frac { 3 } { 7 } e ^ { 11 x }$ 
A)  $- 3 e ^ { 11 x }$ 
B)  $\frac { 7 } { 4 } e ^ { 28 x }$ 
C)  $\frac { 4 } { 7 } e ^ { 11 x }$ 
D)  $- 3 e ^ { 28 x }$ 
E)  $- \frac { 3 } { 7 } e ^ { 11 x }$

Question 10

Evaluate the determinant.
  $\left| \begin{array} { c c } 
9 & 8 \
- 2 & 8
\end{array} \right|$

Accepted Answer

The answer of Evaluate the determinant.
  \(\left| \begin{array} {...

Question 11

Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix
New Row-Equivalent Matrix $$\left[ \begin{array} { r r r } 
- 1 & - 8 & 5 \
- 8 & 9 & 9
\end{array} \right]$$ $$\left[ \begin{array} { r r r } 
- 17 & 10 & 23 \
- 8 & 9 & 9
\end{array} \right]$$

Accepted Answer

A) Add 2 times R1 to R2. 
B) Add -2 times R1 to R2. 
C) Add 2 times R2 to R1. 
D) Add -2 times R2 to R1. 
E) Add 2 times R1 to R1. 
A) Add 2 times R1 to R2. 
B) Add -2 times R1 to R2. 
C) Add 2 times R2 to R1. 
D) Add -2 times R2 to R1. 
E) Add 2 times R1 to R1.

Question 12

Determine the order of the matrix.   $$\left[ \begin{array} { l l l } 
8 & 5 & 4 \
7 & 8 & 1
\end{array} \right]$$

Accepted Answer

A) 3 × 3 
B) 2 × 2 
C) 3 × 1 
D) 2 × 3 
E) 3 × 2 
A) 3 × 3 
B) 2 × 2 
C) 3 × 1 
D) 2 × 3 
E) 3 × 2

Question 13

Solve the system of linear equations.   $$\left\{ \begin{array} { c } 
x + y + z = - 7 \
3 x + 5 y + 4 z = 8 \
3 x + 6 y + 5 z = 0
\end{array} \right.$$

Accepted Answer

A)   $( 2,37 , - 45 )$ 
B)   $( - 1,37 , - 45 )$ 
C)   $( - 1 , - 37 , - 45 )$ 
D)   $( 1,37 , - 45 )$ 
E)   $( 1,38 , - 45 )$ 
A)   $( 2,37 , - 45 )$ 
B)   $( - 1,37 , - 45 )$ 
C)   $( - 1 , - 37 , - 45 )$ 
D)   $( 1,37 , - 45 )$ 
E)   $( 1,38 , - 45 )$

Question 14

Of the products AB, BA, A2 and B2, which ones are possible for the given matrices? $A = \left[ \begin{array} { c } 
- 3 \
1 \
- 7
\end{array} \right] , B = \left[ \begin{array} { l l l } 
7 & 1 & 6
\end{array} \right]$

Accepted Answer

A) B2 only 
B) A2 only 
C) BA only 
D) AB only 
E) AB and BA only 
A) B2 only 
B) A2 only 
C) BA only 
D) AB only 
E) AB and BA only

Question 15

Evaluate the determinant.
  $\left| \begin{array} { c c c c } 
5 & 5 & - 4 & 2 \
4 & 1 & - 4 & 1 \
- 1 & 2 & 1 & - 4 \
1 & 2 & - 5 & - 1
\end{array} \right|$

Accepted Answer

The answer of Evaluate the determinant.
  \(\left| \begin{array} {...

Question 16

Find A + B.   $A = \left[ \begin{array} { l l } 
1 & 2 \
2 & 1
\end{array} \right] , B = \left[ \begin{array} { c c } 
- 4 & - 4 \
5 & 4
\end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { c c } 
- 3 & - 2 \
7 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
- 1 & 5 \
7 & - 2
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
1 & - 2 \
5 & 7
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
- 5 & - 2 \
7 & 5
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
- 7 & - 2 \
7 & 5
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c } 
- 3 & - 2 \
7 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
- 1 & 5 \
7 & - 2
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
1 & - 2 \
5 & 7
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
- 5 & - 2 \
7 & 5
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
- 7 & - 2 \
7 & 5
\end{array} \right]$

Question 17

Of the products AB, BA, A2 and B2, which ones are possible for the given matrices? $$A = \left[ \begin{array} { l l } 
1 & 1 \
6 & 5
\end{array} \right] , B = \left[ \begin{array} { c c } 
5 & - 6 \
- 7 & 3
\end{array} \right]$$

Accepted Answer

A) AB only 
B) AB and BA only 
C) BA only 
D) A2 and B2 only 
E) AB, BA, A2 and B2 
A) AB only 
B) AB and BA only 
C) BA only 
D) A2 and B2 only 
E) AB, BA, A2 and B2

Question 18

Find the determinant of the matrix.   $\left[ \begin{array} { c c } 
- 4 & 0 \
5 & 8
\end{array} \right]$

Accepted Answer

A) 32 
B)  $- 32$ 
C)  $- \frac { 1 } { 32 }$ 
D) 0 
E)  $\frac { 1 } { 32 }$ 
A) 32 
B)  $- 32$ 
C)  $- \frac { 1 } { 32 }$ 
D) 0 
E)  $\frac { 1 } { 32 }$

Question 19

Evaluate the expression. $$\left[ \begin{array} { c c } 
3 & - 4 \
- 1 & 5
\end{array} \right] \left[ \begin{array} { l l } 
- 5 & 2 \
- 4 & 1
\end{array} \right] \left[ \begin{array} { c c } 
- 1 & - 2 \
2 & 4
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } 
15 & 16 \
8 & 20
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
3 & 6 \
21 & 42
\end{array} \right]$ 
C) not possible 
D)  $\left[ \begin{array} { r r } 
27 & - 72 \
- 2 & - 20
\end{array} \right]$ 
E)  $\left[ \begin{array} { l l } 
3 & 21 \
6 & 42
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c } 
15 & 16 \
8 & 20
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
3 & 6 \
21 & 42
\end{array} \right]$ 
C) not possible 
D)  $\left[ \begin{array} { r r } 
27 & - 72 \
- 2 & - 20
\end{array} \right]$ 
E)  $\left[ \begin{array} { l l } 
3 & 21 \
6 & 42
\end{array} \right]$

Question 20

Use Cramer's Rule to solve (if possible) the system of equations.   $$\left\{ \begin{array} { l } 
4 x - 2 y + z = - 3 \
2 x + 2 y + 3 z = 9 \
5 x - 2 y + 6 z = - 15
\end{array} \right.$$

Accepted Answer

A) (3, -6, -3) 
B) (3, 6, -3) 
C) (-3, 6, -3) 
D) (-3, -6, -3) 
E) (7, -6, -3) 
A) (3, -6, -3) 
B) (3, 6, -3) 
C) (-3, 6, -3) 
D) (-3, -6, -3) 
E) (7, -6, -3)

Find the inverse of the matrix. $\left[ \begin{array} { l l l } 1 & 5 & 2 \\0 & 1 & 5 \\0 & 0 & 1\end{array} \right]$

Write the system of linear equations as a matrix equation, AX = B. $\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } & = 18 \\- x _ { 1 } + 3 x _ { 2 } - x _ { 3 } & = 18 \\3 x _ { 1 } - 3 x _ { 2 } + 3 x _ { 3 } & = 18\end{aligned} \right.$

Use the matrix capabilities of a graphing utility to find the determinant of the matrix $\left[ \begin{array} { c c c } 16 & 24 & 8 \\0 & 40 & - 16 \\0 & 0 & - 16\end{array} \right]$ .

Find the determinant of the matrix. $\left[ \begin{array} { c c } 2 & - 2 \\8 & - 16\end{array} \right]$

Use Cramer's rule to find the solution of the system, if possible. $\left\{ \begin{aligned}5 x - y & = 12 \\x + y & = 0\end{aligned} \right.$

Write the matrix in reduced row-echelon form. $\left[ \begin{array} { r r r r } 5 & - 7 & - 3 & 6 \\- 6 & - 6 & 2 & - 44 \\2 & - 4 & - 2 & - 4\end{array} \right]$

Determine whether the matrix is in row-echelon form.If it is, determine if it is also in reduced row-echelon form. $\left[ \begin{array} { r r r r } 1 & 9 & - 9 & - 6 \\0 & 1 & 0 & - 2 \\0 & 0 & 1 & 1\end{array} \right]$

Evaluate the determinant \mid 7 4 in which the entries are functions.

Evaluate the determinant. $\left| \begin{array} { c c } 9 & 8 \\- 2 & 8\end{array} \right|$

Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } - 1 & - 8 & 5 \\- 8 & 9 & 9\end{array} \right]$ $\left[ \begin{array} { r r r } - 17 & 10 & 23 \\- 8 & 9 & 9\end{array} \right]$

Determine the order of the matrix. $\left[ \begin{array} { l l l } 8 & 5 & 4 \\7 & 8 & 1\end{array} \right]$

Solve the system of linear equations. $\left\{ \begin{array} { c } x + y + z = - 7 \\3 x + 5 y + 4 z = 8 \\3 x + 6 y + 5 z = 0\end{array} \right.$

Of the products AB, BA, A² and B², which ones are possible for the given matrices? $A = \left[ \begin{array} { c } - 3 \\1 \\- 7\end{array} \right] , B = \left[ \begin{array} { l l l } 7 & 1 & 6\end{array} \right]$

Evaluate the determinant. $\left| \begin{array} { c c c c } 5 & 5 & - 4 & 2 \\4 & 1 & - 4 & 1 \\- 1 & 2 & 1 & - 4 \\1 & 2 & - 5 & - 1\end{array} \right|$

Find A + B. $A = \left[ \begin{array} { l l } 1 & 2 \\2 & 1\end{array} \right] , B = \left[ \begin{array} { c c } - 4 & - 4 \\5 & 4\end{array} \right]$

Of the products AB, BA, A² and B², which ones are possible for the given matrices? $A = \left[ \begin{array} { l l } 1 & 1 \\6 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 5 & - 6 \\- 7 & 3\end{array} \right]$

Find the determinant of the matrix. $\left[ \begin{array} { c c } - 4 & 0 \\5 & 8\end{array} \right]$

Evaluate the expression. $\left[ \begin{array} { c c } 3 & - 4 \\- 1 & 5\end{array} \right] \left[ \begin{array} { l l } - 5 & 2 \\- 4 & 1\end{array} \right] \left[ \begin{array} { c c } - 1 & - 2 \\2 & 4\end{array} \right]$

Use Cramer's Rule to solve (if possible) the system of equations. $\left\{ \begin{array} { l } 4 x - 2 y + z = - 3 \\2 x + 2 y + 3 z = 9 \\5 x - 2 y + 6 z = - 15\end{array} \right.$

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Exam 8: Matrices and Determinants

Find the inverse of the matrix. [152015001]\left[ \begin{array} { l l l } 1 & 5 & 2 \\0 & 1 & 5 \\0 & 0 & 1\end{array} \right]​100​510​251​​

Use the matrix capabilities of a graphing utility to find the determinant of the matrix [16248040−1600−16]\left[ \begin{array} { c c c } 16 & 24 & 8 \\0 & 40 & - 16 \\0 & 0 & - 16\end{array} \right]​1600​24400​8−16−16​​ .

Find the determinant of the matrix. [2−28−16]\left[ \begin{array} { c c } 2 & - 2 \\8 & - 16\end{array} \right][28​−2−16​]

Use Cramer's rule to find the solution of the system, if possible. {5x−y=12x+y=0\left\{ \begin{aligned}5 x - y & = 12 \\x + y & = 0\end{aligned} \right.{5x−yx+y​=12=0​

Write the matrix in reduced row-echelon form. [5−7−36−6−62−442−4−2−4]\left[ \begin{array} { r r r r } 5 & - 7 & - 3 & 6 \\- 6 & - 6 & 2 & - 44 \\2 & - 4 & - 2 & - 4\end{array} \right]​5−62​−7−6−4​−32−2​6−44−4​​

Determine whether the matrix is in row-echelon form.If it is, determine if it is also in reduced row-echelon form. [19−9−6010−20011]\left[ \begin{array} { r r r r } 1 & 9 & - 9 & - 6 \\0 & 1 & 0 & - 2 \\0 & 0 & 1 & 1\end{array} \right]​100​910​−901​−6−21​​