Question 1

Use the Gauss-Jordan method to solve the system of equations.
-$7 x-y-7 z=4$
$-7 x+3 z=-39$
$7 y+z=29$

Accepted Answer

A)  $(-9,3,18)$ 
B)  No solution 
C)  $(9,3,8)$ 
D)  $(9,8,3)$ 
A)  $(-9,3,18)$ 
B)  No solution 
C)  $(9,3,8)$ 
D)  $(9,8,3)$

Question 2

Write the word or phrase that best completes each statement or answers the question
-Using the matrices $L=\left[\begin{array}{lll}1 & m & n \ p & q & r\end{array}\right]$ and $O=\left[\begin{array}{lll}0 & 0 & 0 \ 0 & 0 & 0\end{array}\right]$, verify that $L+O=L$.

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Solve the matrix equation for $X$.}
-$\mathrm{A}=\left[\begin{array}{rrr}2 & 2 & 0 \ -4 & -3 & 2 \ 0 & -3 & -5\end{array}\right], \mathrm{B}=\left[\begin{array}{r}4 \ -7 \ 2\end{array}\right], \mathrm{AX}=\mathrm{B}$

Accepted Answer

A) $\left[\begin{array}{r}11 \ -9 \ 5\end{array}\right]$ 
B) $\left[\begin{array}{r}11 \ -9 \ 3\end{array}\right]$ 
C) $\left[\begin{array}{r}11 \ -10 \ 6\end{array}\right]$ 
D)  $\left[\begin{array}{r}13 \ -8 \ 5\end{array}\right]$ 
A) $\left[\begin{array}{r}11 \ -9 \ 5\end{array}\right]$ 
B) $\left[\begin{array}{r}11 \ -9 \ 3\end{array}\right]$ 
C) $\left[\begin{array}{r}11 \ -10 \ 6\end{array}\right]$ 
D)  $\left[\begin{array}{r}13 \ -8 \ 5\end{array}\right]$

Question 4

Solve the system of equations. If the system is dependent, express solutions in terms of the parameter $\mathrm{z}$.
-$x-y+z=1$
$x+y+z=-5$
$\mathrm{x}+\mathrm{y}-\mathrm{z}=-11$

Accepted Answer

A)  $(3,-5,-3)$ 
B)  $(-5,3,-3)$ 
C)  $(-5,-3,3)$ 
D)  No solution 
A)  $(3,-5,-3)$ 
B)  $(-5,3,-3)$ 
C)  $(-5,-3,3)$ 
D)  No solution

Question 5

Write a matrix to display the information.
-Factory A makes 10 model-A, 8 model-D, and 6 model-M train sets. Factory B makes 5 model-A, 7 model-D, and 5 model-M train sets. If model-A sells for $\$ 19$, model-D for $\$ 22$, and model-M for $\$ 30$, write a $2 \times 3$ matrix to summarize the income by model.

Accepted Answer

A) $\left[\begin{array}{lll}190 & 152 & 114 \ 110 & 154 & 110\end{array}\right]$ 
B) $\left[\begin{array}{rr}190 & 95 \ 176 & 154 \ 180 & 150\end{array}\right]$ 
C) $\left[\begin{array}{rrr}190 & 176 & 180 \ 95 & 154 & 150\end{array}\right]$ 
D) $\left[\begin{array}{ll}190 & 110 \ 152 & 154 \ 114 & 110\end{array}\right]$ 
A) $\left[\begin{array}{lll}190 & 152 & 114 \ 110 & 154 & 110\end{array}\right]$ 
B) $\left[\begin{array}{rr}190 & 95 \ 176 & 154 \ 180 & 150\end{array}\right]$ 
C) $\left[\begin{array}{rrr}190 & 176 & 180 \ 95 & 154 & 150\end{array}\right]$ 
D) $\left[\begin{array}{ll}190 & 110 \ 152 & 154 \ 114 & 110\end{array}\right]$

Question 6

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent.
-$x-y+z=-6$
$2 x+y+z=0$
$-x+y-z=15$

Accepted Answer

A)  Dependent 
B)  Inconsistent 
C)  Independent 
A)  Dependent 
B)  Inconsistent 
C)  Independent

Question 7

Perform the indicated operation.
-Let $A=\left[\begin{array}{ll}3 & 3 \ 2 & 4\end{array}\right]$ and $B=\left[\begin{array}{rr}0 & 4 \ -1 & 6\end{array}\right]$. Find $4 A+B$.

Accepted Answer

A) $\left[\begin{array}{rr}12 & 7 \ 7 & 10\end{array}\right]$ 
B) $\left[\begin{array}{rr}12 & 28 \ 4 & 40\end{array}\right]$ 
C) $\left[\begin{array}{rr}12 & 16 \ 1 & 10\end{array}\right]$ 
D)  $\left[\begin{array}{rr}12 & 16 \ 7 & 22\end{array}\right]$ 
A) $\left[\begin{array}{rr}12 & 7 \ 7 & 10\end{array}\right]$ 
B) $\left[\begin{array}{rr}12 & 28 \ 4 & 40\end{array}\right]$ 
C) $\left[\begin{array}{rr}12 & 16 \ 1 & 10\end{array}\right]$ 
D)  $\left[\begin{array}{rr}12 & 16 \ 7 & 22\end{array}\right]$

Question 8

Perform the row operations on the matrix and write the resulting matrix.
-Replace $R_{3}$ by $\frac{1}{2} R_{1}+R_{2}$
$\left[\begin{array}{rrr|r}2 & 2 & 4 & 6 \ 1 & -1 & -2 & 5 \ 0 & 1 & 0 & 1\end{array}\right]$

Accepted Answer

A) $\left[\begin{array}{rrr|r}
2 & 2 & 4 & 6 \
1 & -1 & -2 & 5 \
2 & 0 & 0 & 8
\end{array}\right]$ 
B) $\left[\begin{array}{lll|r}1 & 1 & 2 & 3 \ 2 & 0 & 0 & 8 \ 0 & 1 & 0 & 1\end{array}\right]$ 
C)  $\left[\begin{array}{lll|r}2 & 2 & 4 & 6 \ 0 & 1 & 0 & 1 \ 3 & 1 & 2 & 11\end{array}\right]$ 
D)  $\left[\begin{array}{lll|l}1 & 1 & 2 & 3 \ 0 & 1 & 0 & 0 \ 2 & 0 & 0 & 8\end{array}\right]$ 
A) $\left[\begin{array}{rrr|r}
2 & 2 & 4 & 6 \
1 & -1 & -2 & 5 \
2 & 0 & 0 & 8
\end{array}\right]$ 
B) $\left[\begin{array}{lll|r}1 & 1 & 2 & 3 \ 2 & 0 & 0 & 8 \ 0 & 1 & 0 & 1\end{array}\right]$ 
C)  $\left[\begin{array}{lll|r}2 & 2 & 4 & 6 \ 0 & 1 & 0 & 1 \ 3 & 1 & 2 & 11\end{array}\right]$ 
D)  $\left[\begin{array}{lll|l}1 & 1 & 2 & 3 \ 0 & 1 & 0 & 0 \ 2 & 0 & 0 & 8\end{array}\right]$

Question 9

Solve the problem by writing and solving a suitable system of equations.
-A company produces three models of video cassette player, models $X, Y$, and Z. Each model $X$ machine requires 3.2 hours of electronics work, 2.8 hours of assembly time, and 4.4 hours of quality assurance time. Each model $\mathrm{Y}$ machine requires 5.2 hours of electronics work, 4.4 hours of assembly time, and 5.2 hours of quality assurance time. Each model $\mathrm{Z}$ machine requires 5.2 hours of electronics work, 3.2 hours of assembly time, and 3.8 hours of quality assurance time. There are 440 hours available each week for electronics, 346 hours for assembly, and 453 hours for quality assurance. How many of each model should be produced each week if all available time must be used?

Accepted Answer

A)  38 model $X$, 37 model Y, 25 model $Z$ 
B)  41 model X, 35 model Y, 24 model Z 
C)  40 model $X$, 30 model $Y, 30$ model $Z$ 
D)  40 model $X$, 35 model Y, 25 model Z 
A)  38 model $X$, 37 model Y, 25 model $Z$ 
B)  41 model X, 35 model Y, 24 model Z 
C)  40 model $X$, 30 model $Y, 30$ model $Z$ 
D)  40 model $X$, 35 model Y, 25 model Z

Question 10

Solve the system of two equations in two variables.
-$x+9 y=-18$
$8 x+10 y=-20$

Accepted Answer

A)  No solution 
B)  $(0,-2)$ 
C)  $(2,0)$ 
D)  $(1,-3)$ 
A)  No solution 
B)  $(0,-2)$ 
C)  $(2,0)$ 
D)  $(1,-3)$

Question 11

Given the matrices $A$ and $B$, find the matrix product $A B$.
-$\mathrm{A}=\left[\begin{array}{rrr}7 & 3 & 6 \ -6 & -4 & 1 \ -1 & 3 & 8\end{array}\right], \mathrm{B}=\left[\begin{array}{rrr}-4 & 6 & 4 \ 2 & -7 & -6 \ -8 & -9 & -5\end{array}\right]$. Find $\mathrm{AB}$.

Accepted Answer

A) $\left[\begin{array}{rrr}-28 & 18 & 24 \ -12 & 28 & -6 \ 8 & -27 & -40\end{array}\right]$ 
B) $$\left[\begin{array}{rrr}
-70 & -33 & -20 \
8 & -17 & -5 \
-54 & -99 & -62
\end{array}\right]$$ 
C) $$\left[\begin{array}{lrl}
-70 & 8 & -54 \
-33 & -17 & -99 \
-20 & -5 & -62
\end{array}\right]$$ 
D) $$\left[\begin{array}{rrr}
7 & 3 & 6 \
-6 & -4 & 1 \
-1 & 3 & 8 \
-4 & 6 & 4 \
2 & -7 & -6 \
-8 & -9 & -5
\end{array}\right]$$ 
A) $\left[\begin{array}{rrr}-28 & 18 & 24 \ -12 & 28 & -6 \ 8 & -27 & -40\end{array}\right]$ 
B) $$\left[\begin{array}{rrr}
-70 & -33 & -20 \
8 & -17 & -5 \
-54 & -99 & -62
\end{array}\right]$$ 
C) $$\left[\begin{array}{lrl}
-70 & 8 & -54 \
-33 & -17 & -99 \
-20 & -5 & -62
\end{array}\right]$$ 
D) $$\left[\begin{array}{rrr}
7 & 3 & 6 \
-6 & -4 & 1 \
-1 & 3 & 8 \
-4 & 6 & 4 \
2 & -7 & -6 \
-8 & -9 & -5
\end{array}\right]$$

Question 12

Solve the system of two equations in two variables.
-$x-3 y=10$
$-7 x-4 y=30$

Accepted Answer

A)  $(2,-3)$ 
B)  $(-2,-4)$ 
C)  No solution 
D)  $(-3,-3)$ 
A)  $(2,-3)$ 
B)  $(-2,-4)$ 
C)  No solution 
D)  $(-3,-3)$

Question 13

Solve the problem by writing and solving a suitable system of equations.
-Barges from ports $X$ and $Y$ went to cities $A$ and $B$. $X$ sent 30 barges and $Y$ sent 8 . City A needs 21 barges and B needs 17. Shipping costs $\$ 220$ from $X$ to $A, \$ 300$ from $X$ to $B, \$ 400$ from $Y$ to $A$, and $\$ 180$ from $Y$ to B. $\$ 8760$ was spent. How many barges went where?

Accepted Answer

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

Question 14

Obtain an equivalent system by performing the stated elementary operation on the system.
-Multiply the second equation by -1 .
$x-5 y+z=5$
$3 x-3 y-z=-18$
$5 x+y+4 z=-12$
$x-3 y+z=-7$

Accepted Answer

A)  x - 5y + z = 5
-3x + 3y + z = 18
5x + y + 4z = -12
X - 3y + z = -7 
B)  x - 5y + z = 5
-3x - 3y - z = -18
5x + y + 4z = -12
X - 3y + z = -7 
C)  x - 5y + z = 5
-3x + 3y + z = -18
5x + y + 4z = -12
X - 3y + z = -7 
D)  -x + 5y - z = -5
3x - 3y - z = -18
5x + y + 4z = -12
X - 3y + z = -7 
A)  x - 5y + z = 5
-3x + 3y + z = 18
5x + y + 4z = -12
X - 3y + z = -7 
B)  x - 5y + z = 5
-3x - 3y - z = -18
5x + y + 4z = -12
X - 3y + z = -7 
C)  x - 5y + z = 5
-3x + 3y + z = -18
5x + y + 4z = -12
X - 3y + z = -7 
D)  -x + 5y - z = -5
3x - 3y - z = -18
5x + y + 4z = -12
X - 3y + z = -7

Question 15

The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of thesystem.
-$\left[\begin{array}{rrrrr|r}1 & 0 & 0 & 0 & 0 & 2 \ 0 & 1 & 0 & 0 & 0 & 8 \ 0 & 0 & 1 & 0 & 0 & 4 \ 0 & 0 & 0 & 1 & 0 & -4 \ 0 & 0 & 0 & 0 & 0 & 1\end{array}\right]$

Accepted Answer

A)  $(2,8,4,-4,1)$ 
B)  $(2,8,4,-4, w)$ for any real number $\mathrm{w}$ 
C)  $(2,8,4,-4)$ 
D)  No solution 
A)  $(2,8,4,-4,1)$ 
B)  $(2,8,4,-4, w)$ for any real number $\mathrm{w}$ 
C)  $(2,8,4,-4)$ 
D)  No solution

Question 16

Find the inverse, if it exists, of the given matrix.
-$\mathrm{A}=\left[\begin{array}{rr} 1 & -3 \ -5 & 0\end{array}\right]$

Accepted Answer

A) $\left[\begin{array}{cc}0 & \frac{1}{5} \ \frac{1}{3} & -\frac{1}{15}\end{array}\right]$ 
B)  $\left[\begin{array}{cc}0 & -\frac{1}{5} \ -\frac{1}{3} & -\frac{1}{15}\end{array}\right]$ 
C)  $\left[\begin{array}{rr}-\frac{1}{3} & -\frac{1}{15} \ 0 & -\frac{1}{5}\end{array}\right]$ 
D)  $\left[\begin{array}{rr}-\frac{1}{15} & -\frac{1}{5} \ -\frac{1}{3} & 0\end{array}\right]$ 
A) $\left[\begin{array}{cc}0 & \frac{1}{5} \ \frac{1}{3} & -\frac{1}{15}\end{array}\right]$ 
B)  $\left[\begin{array}{cc}0 & -\frac{1}{5} \ -\frac{1}{3} & -\frac{1}{15}\end{array}\right]$ 
C)  $\left[\begin{array}{rr}-\frac{1}{3} & -\frac{1}{15} \ 0 & -\frac{1}{5}\end{array}\right]$ 
D)  $\left[\begin{array}{rr}-\frac{1}{15} & -\frac{1}{5} \ -\frac{1}{3} & 0\end{array}\right]$

Question 17

Solve the system of equations. If the system is dependent, express solutions in terms of the parameter $\mathrm{z}$.
-$-2 x+4 y+7 z=8$
$7 \mathrm{x}+\mathrm{y}-6 \mathrm{z}=15$

Accepted Answer

A)  $\left(\frac{26}{15}+\frac{31}{30} z, 15+7 x-6 z, z\right)$ 
B)  $\left(\frac{26}{15}+\frac{31}{30} z, 15-7 x+6 z, z\right)$ 
C)  $\left(\frac{26}{15}+\frac{31}{30} z, \frac{43}{15}-\frac{37}{30} z, z\right)$ 
D)  $(-52-31 z,-86-52 z, z)$ 
A)  $\left(\frac{26}{15}+\frac{31}{30} z, 15+7 x-6 z, z\right)$ 
B)  $\left(\frac{26}{15}+\frac{31}{30} z, 15-7 x+6 z, z\right)$ 
C)  $\left(\frac{26}{15}+\frac{31}{30} z, \frac{43}{15}-\frac{37}{30} z, z\right)$ 
D)  $(-52-31 z,-86-52 z, z)$

Question 18

Perform the row operations on the matrix and write the resulting matrix.
-Replace $R_{2}$ by $R_{1}+R_{2}$
$\left[\begin{array}{rr|r}1 & 0 & 2 \ -1 & 1 & 3\end{array}\right]$

Accepted Answer

A) $\left[\begin{array}{ll|l}1 & 0 & 2 \ 0 & 0 & 5\end{array}\right]$ 
B) $\left[\begin{array}{ll|l}1 & 0 & 2 \ 0 & 1 & 5\end{array}\right]$ 
C) $\left[\begin{array}{rr|r}0 & 1 & 5 \ -1 & 1 & 3\end{array}\right]$ 
D) $\left[\begin{array}{rr|r}1 & 0 & 2 \ -1 & 1 & 3\end{array}\right]$ 
A) $\left[\begin{array}{ll|l}1 & 0 & 2 \ 0 & 0 & 5\end{array}\right]$ 
B) $\left[\begin{array}{ll|l}1 & 0 & 2 \ 0 & 1 & 5\end{array}\right]$ 
C) $\left[\begin{array}{rr|r}0 & 1 & 5 \ -1 & 1 & 3\end{array}\right]$ 
D) $\left[\begin{array}{rr|r}1 & 0 & 2 \ -1 & 1 & 3\end{array}\right]$

Question 19

Determine whether the given ordered set of numbers is a solution of the system of equations.
-$(-1,2)$
$4 x+y=-2$
$2 x+4 y=6$

Accepted Answer

A) True 
 B)False

Question 20

Solve the problem by writing and solving a suitable system of equations.
-Suppose that you are to cut a piece of ribbon for a wreath that is 161 inches long into two pieces so that one piece is 6 times as long as the other. How long is each piece of ribbon?

Accepted Answer

A)  23 and 161 inches 
B)  27 and 161 inches 
C)  27 and 115 inches 
D)  23 and 138 inches 
A)  23 and 161 inches 
B)  27 and 161 inches 
C)  27 and 115 inches 
D)  23 and 138 inches

Use the Gauss-Jordan method to solve the system of equations. - $7 x-y-7 z=4$ $-7 x+3 z=-39$ $7 y+z=29$

Write the word or phrase that best completes each statement or answers the question -Using the matrices $L=\left[\begin{array}{lll}1 & m & n \\ p & q & r\end{array}\right]$ and $O=\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$ , verify that $L+O=L$ .

Solve the matrix equation for $X$ .} - $\mathrm{A}=\left[\begin{array}{rrr}2 & 2 & 0 \\ -4 & -3 & 2 \\ 0 & -3 & -5\end{array}\right], \mathrm{B}=\left[\begin{array}{r}4 \\ -7 \\ 2\end{array}\right], \mathrm{AX}=\mathrm{B}$

Solve the system of equations. If the system is dependent, express solutions in terms of the parameter $\mathrm{z}$ . - $x-y+z=1$ $x+y+z=-5$ $\mathrm{x}+\mathrm{y}-\mathrm{z}=-11$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x-y+z=-6$ $2 x+y+z=0$ $-x+y-z=15$

Perform the indicated operation. -Let $A=\left[\begin{array}{ll}3 & 3 \\ 2 & 4\end{array}\right]$ and $B=\left[\begin{array}{rr}0 & 4 \\ -1 & 6\end{array}\right]$ . Find $4 A+B$ .

Perform the row operations on the matrix and write the resulting matrix. -Replace $R_{3}$ by $\frac{1}{2} R_{1}+R_{2}$ $\left[\begin{array}{rrr|r}2 & 2 & 4 & 6 \\ 1 & -1 & -2 & 5 \\ 0 & 1 & 0 & 1\end{array}\right]$

Solve the system of two equations in two variables. - $x+9 y=-18$ $8 x+10 y=-20$

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $\mathrm{A}=\left[\begin{array}{rrr}7 & 3 & 6 \\ -6 & -4 & 1 \\ -1 & 3 & 8\end{array}\right], \mathrm{B}=\left[\begin{array}{rrr}-4 & 6 & 4 \\ 2 & -7 & -6 \\ -8 & -9 & -5\end{array}\right]$ . Find $\mathrm{AB}$ .

Solve the system of two equations in two variables. - $x-3 y=10$ $-7 x-4 y=30$

Obtain an equivalent system by performing the stated elementary operation on the system. -Multiply the second equation by -1 . $x-5 y+z=5$ $3 x-3 y-z=-18$ $5 x+y+4 z=-12$ $x-3 y+z=-7$

The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of thesystem. - $\left[\begin{array}{rrrrr|r}1 & 0 & 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 & 0 & 8 \\ 0 & 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 0 & 1 & 0 & -4 \\ 0 & 0 & 0 & 0 & 0 & 1\end{array}\right]$

Find the inverse, if it exists, of the given matrix. - $\mathrm{A}=\left[\begin{array}{rr} 1 & -3 \\ -5 & 0\end{array}\right]$

Solve the system of equations. If the system is dependent, express solutions in terms of the parameter $\mathrm{z}$ . - $-2 x+4 y+7 z=8$ $7 \mathrm{x}+\mathrm{y}-6 \mathrm{z}=15$

Perform the row operations on the matrix and write the resulting matrix. -Replace $R_{2}$ by $R_{1}+R_{2}$ $\left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right]$

Determine whether the given ordered set of numbers is a solution of the system of equations. - $(-1,2)$ $4 x+y=-2$ $2 x+4 y=6$

Solve the problem by writing and solving a suitable system of equations. -Suppose that you are to cut a piece of ribbon for a wreath that is 161 inches long into two pieces so that one piece is 6 times as long as the other. How long is each piece of ribbon?

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Exam 6: Systems of Linear Equations and Matrices

Use the Gauss-Jordan method to solve the system of equations. - 7x−y−7z=47 x-y-7 z=47x−y−7z=4 −7x+3z=−39-7 x+3 z=-39−7x+3z=−39 7y+z=297 y+z=297y+z=29

Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z\mathrm{z}z . - x−y+z=1x-y+z=1x−y+z=1 x+y+z=−5x+y+z=-5x+y+z=−5 x+y−z=−11\mathrm{x}+\mathrm{y}-\mathrm{z}=-11x+y−z=−11

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - x−y+z=−6x-y+z=-6x−y+z=−6 2x+y+z=02 x+y+z=02x+y+z=0 −x+y−z=15-x+y-z=15−x+y−z=15

Perform the indicated operation. -Let A=[3324]A=\left[\begin{array}{ll}3 & 3 \\ 2 & 4\end{array}\right]A=[32​34​] and B=[04−16]B=\left[\begin{array}{rr}0 & 4 \\ -1 & 6\end{array}\right]B=[0−1​46​] . Find 4A+B4 A+B4A+B .

Perform the row operations on the matrix and write the resulting matrix. -Replace R3R_{3}R3​ by 12R1+R2\frac{1}{2} R_{1}+R_{2}21​R1​+R2​ [22461−1−250101]\left[\begin{array}{rrr|r}2 & 2 & 4 & 6 \\ 1 & -1 & -2 & 5 \\ 0 & 1 & 0 & 1\end{array}\right]​210​2−11​4−20​651​​

Solve the system of two equations in two variables. - x+9y=−18x+9 y=-18x+9y=−18 8x+10y=−208 x+10 y=-208x+10y=−20

Solve the system of two equations in two variables. - x−3y=10x-3 y=10x−3y=10 −7x−4y=30-7 x-4 y=30−7x−4y=30

Obtain an equivalent system by performing the stated elementary operation on the system. -Multiply the second equation by -1 . x−5y+z=5x-5 y+z=5x−5y+z=5 3x−3y−z=−183 x-3 y-z=-183x−3y−z=−18 5x+y+4z=−125 x+y+4 z=-125x+y+4z=−12 x−3y+z=−7x-3 y+z=-7x−3y+z=−7

Find the inverse, if it exists, of the given matrix. - A=[1−3−50]\mathrm{A}=\left[\begin{array}{rr} 1 & -3 \\ -5 & 0\end{array}\right]A=[1−5​−30​]

Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z\mathrm{z}z . - −2x+4y+7z=8-2 x+4 y+7 z=8−2x+4y+7z=8 7x+y−6z=157 \mathrm{x}+\mathrm{y}-6 \mathrm{z}=157x+y−6z=15

Perform the row operations on the matrix and write the resulting matrix. -Replace R2R_{2}R2​ by R1+R2R_{1}+R_{2}R1​+R2​ [102−113]\left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right][1−1​01​23​]

Determine whether the given ordered set of numbers is a solution of the system of equations. - (−1,2)(-1,2)(−1,2) 4x+y=−24 x+y=-24x+y=−2 2x+4y=62 x+4 y=62x+4y=6