Question 1

Perform the elementary row operation on the given matrix.
-$\begin{array} { l } 
R _ { 2 } \Leftrightarrow R _ { 3 } \
{ \left[ \begin{array} { r r r | r } 
- 8 & 2 & - 9 & - 4 \
- 3 & 7 & - 6 & 6 \
5 & 0 & 3 & 6
\end{array} \right] }
\end{array}$

Accepted Answer

A)  $ \left[\begin{array}{rrr|r}-8 & 2 & -9 & -4 \ 2 & 7 & -3 & 9 \ 5 & 0 & 3 & 6\end{array}\right] $ 
B)  $ \left[\begin{array}{rrr|r}-8 & 2 & -9 & -4 \ 5 & 0 & 3 & 6 \ -3 & 7 & -6 & 6\end{array}\right] $ 
C)  $ \left[\begin{array}{rrr|r}-3 & 7 & -6 & 6 \ -8 & 2 & -9 & -4 \ 5 & 0 & 3 & 6\end{array}\right] $ 
D)  $ \left[\begin{array}{rrr|r}-8 & 2 & -9 & -4 \ -3 & 7 & -6 & 6 \ 2 & 7 & -3 & 9\end{array}\right] $ 
A)  $ \left[\begin{array}{rrr|r}-8 & 2 & -9 & -4 \ 2 & 7 & -3 & 9 \ 5 & 0 & 3 & 6\end{array}\right] $ 
B)  $ \left[\begin{array}{rrr|r}-8 & 2 & -9 & -4 \ 5 & 0 & 3 & 6 \ -3 & 7 & -6 & 6\end{array}\right] $ 
C)  $ \left[\begin{array}{rrr|r}-3 & 7 & -6 & 6 \ -8 & 2 & -9 & -4 \ 5 & 0 & 3 & 6\end{array}\right] $ 
D)  $ \left[\begin{array}{rrr|r}-8 & 2 & -9 & -4 \ -3 & 7 & -6 & 6 \ 2 & 7 & -3 & 9\end{array}\right] $

Question 2

Find B - A.
-$$A = \left[ \begin{array} { r r } 
2 & 6 \
4 & 4 \
2 & - 7
\end{array} \right] , B = \left[ \begin{array} { r r } 
- 7 & 6 \
- 5 & - 4 \
7 & 6
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r } - 5 & 12 \ - 1 & 0 \ 9 & - 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 9 & 0 \ 9 & 8 \ - 5 & - 13 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & 0 \ - 9 & - 8 \ 5 & 13 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 7 & 12 \ - 5 & 0 \ 7 & - 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } - 5 & 12 \ - 1 & 0 \ 9 & - 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 9 & 0 \ 9 & 8 \ - 5 & - 13 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & 0 \ - 9 & - 8 \ 5 & 13 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 7 & 12 \ - 5 & 0 \ 7 & - 1 \end{array} \right]$

Question 3

Explain the meaning of the notation $- R _ { 2 } \rightarrow R _ { 2 }$

Accepted Answer

Multiply row 2 by -1

Question 4

Solve the problem.
-The labor costs per hour for an electrician, plumber, and air-conditioning/heating expert are given in matrix L. The time required from each specialist for three new model homes is given in matrix

Cost/hr
$\begin{array} { l } 
L = \left[ \begin{array} { l } 
\$ 40 \
\$ 38 \
\$ 34
\end{array} \right] \begin{array} { l } 
\text { Electrician } \
\text { Plumber } \
\text { AC/heating }
\end{array} \\
\text { Time(hr) } \
\text { Electrician Plumber AC/heating } \
T = \left[ \begin{array} { l l r l } 
165 & 14 & 16 \
25 & 22 & 19 \
17 & 13 & 8
\end{array} \right] \begin{array} { l } 
\text { Model 1 } \
\text { Model 2 } \
\text { Model 3 }
\end{array} \
\end{array}$

Find a matrix that gives the total cost for these three services for each model.

Accepted Answer

A)  $\left[ \begin{array} { l } \$ 8,128 \ \$ 1,838 \ \$ 1,634 \end{array} \right]$ 
B)  $[ \$ 11,604 ]$ 
C)  $\left[ \begin{array} { l } \$ 7,676 \ \$ 2,482 \ \$ 1,446 \end{array} \right]$ 
D)  $[ \$ 11,600 ]$ 
A)  $\left[ \begin{array} { l } \$ 8,128 \ \$ 1,838 \ \$ 1,634 \end{array} \right]$ 
B)  $[ \$ 11,604 ]$ 
C)  $\left[ \begin{array} { l } \$ 7,676 \ \$ 2,482 \ \$ 1,446 \end{array} \right]$ 
D)  $[ \$ 11,600 ]$

Question 5

Evaluate the determinant of the given matrix and state whether the matrix is invertible.
-$$A = \left[ \begin{array} { r r r } 
- 5 & - 3 & 1 \
- 4 & 3 & - 9 \
- 5 & 6 & 4
\end{array} \right]$$

Accepted Answer

A)  $- 522 , \mathrm { No }$ 
B)  $- 522 , \mathrm { Yes }$ 
C)  $- 156 , \mathrm { No }$ 
D)  $- 156 , \mathrm { Yes }$ 
A)  $- 522 , \mathrm { No }$ 
B)  $- 522 , \mathrm { Yes }$ 
C)  $- 156 , \mathrm { No }$ 
D)  $- 156 , \mathrm { Yes }$

Question 6

Determine whether A and B are inverses.
-$$A = \left[ \begin{array} { r r r } 
0 & 3 & 1 \
1 & - 2 & 0 \
4 & - 1 & 2
\end{array} \right] \text { and } B = \left[ \begin{array} { r r r } 
- 4 & - 7 & 2 \
- 2 & - 4 & 1 \
7 & 12 & - 3
\end{array} \right]$$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 7

Solve the problem.
-  
a. Write a matrix A that represents the coordinates of the triangle. Place the x-coordinate of each point in the first row of A and the corresponding y-coordinate in the second row of A.
b. Use addition of matrices to shift the triangle 5 units to the right and 4 units down.

Accepted Answer

A)  a. $A = \left[ \begin{array} { r r r } - 1 & 1 & 3 \ 1 & 5 & 1 \end{array} \right]$
b. $\left[ \begin{array} { r r r } 4 & 6 & 8 \ - 3 & 1 & - 3 \end{array} \right]$ 
B)  a. $A = \left[ \begin{array} { r r r } - 1 & 1 & 3 \ 1 & 5 & 1 \end{array} \right]$
b. $\left[ \begin{array} { c c c } 4 & 6 & 8 \ 5 & 9 & 5 \end{array} \right]$ 
C)  a. $A = \left[ \begin{array} { c c c } 1 & 5 & 1 \ - 1 & 1 & 3 \end{array} \right]$
b. $\left[ \begin{array} { r r r } - 3 & 1 & - 3 \ 4 & 6 & 8 \end{array} \right]$ 
D)  a. $A = \left[ \begin{array} { r r r } - 1 & 1 & 3 \ 1 & 5 & 1 \end{array} \right]$
b. $\left[ \begin{array} { r r r } - 6 & - 4 & - 2 \ 5 & 9 & 5 \end{array} \right]$ 
A)  a. $A = \left[ \begin{array} { r r r } - 1 & 1 & 3 \ 1 & 5 & 1 \end{array} \right]$
b. $\left[ \begin{array} { r r r } 4 & 6 & 8 \ - 3 & 1 & - 3 \end{array} \right]$ 
B)  a. $A = \left[ \begin{array} { r r r } - 1 & 1 & 3 \ 1 & 5 & 1 \end{array} \right]$
b. $\left[ \begin{array} { c c c } 4 & 6 & 8 \ 5 & 9 & 5 \end{array} \right]$ 
C)  a. $A = \left[ \begin{array} { c c c } 1 & 5 & 1 \ - 1 & 1 & 3 \end{array} \right]$
b. $\left[ \begin{array} { r r r } - 3 & 1 & - 3 \ 4 & 6 & 8 \end{array} \right]$ 
D)  a. $A = \left[ \begin{array} { r r r } - 1 & 1 & 3 \ 1 & 5 & 1 \end{array} \right]$
b. $\left[ \begin{array} { r r r } - 6 & - 4 & - 2 \ 5 & 9 & 5 \end{array} \right]$

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An $n \times m$ matrix whose elements are all zero is called a ________matrix.

Accepted Answer

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

Question 9

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The symbol $I _ { n }$ represents the ________matrix of order n.

Accepted Answer

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

Question 10

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { l } 
4 x - 5 y = - 11 \
- 2 x + 3 y = 5
\end{array}$$

Accepted Answer

A)  $\{ ( 4,1 ) \}$ 
B)  $\{ ( - 1 , - 4 ) \}$ 
C)  $\{ ( - 4 , - 1 ) \}$ 
D)  $\{ ( 1,4 ) \}$ 
A)  $\{ ( 4,1 ) \}$ 
B)  $\{ ( - 1 , - 4 ) \}$ 
C)  $\{ ( - 4 , - 1 ) \}$ 
D)  $\{ ( 1,4 ) \}$

Question 11

Given the matrices A and B, solve for X.
-$$5 X - B = A$$
$A = \left[ \begin{array} { r r } - 3 & 5 \ - 3 & - 4 \end{array} \right]$ and $B = \left[ \begin{array} { l l } - 3 & 4 \ - 3 & 5 \end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { r r } 0 & 1 \ 0 & - 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } - \frac { 6 } { 5 } & \frac { 1 } { 5 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } - 6 & 9 \ - 6 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & - \frac { 9 } { 5 } \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 0 & 1 \ 0 & - 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } - \frac { 6 } { 5 } & \frac { 1 } { 5 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } - 6 & 9 \ - 6 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & - \frac { 9 } { 5 } \end{array} \right]$

Question 12

Solve the system using Gaussian elimination or Gauss-Jordan elimination.
-$$\begin{aligned}
x + 4 y & = - 7 \
4 x + 3 y & = 11
\end{aligned}$$

Accepted Answer

A)  $\{ ( 5 , - 3 ) \}$ 
B)  $\left\{ \left( \frac { 17 } { 19 } , \frac { 65 } { 19 } \right) \right\}$ 
C)  $\{ ( - 3,5 ) \}$ 
D)  $\left\{ \left\{ - \frac { 65 } { 19 } , - \frac { 17 } { 19 } \right) \right\}$ 
A)  $\{ ( 5 , - 3 ) \}$ 
B)  $\left\{ \left( \frac { 17 } { 19 } , \frac { 65 } { 19 } \right) \right\}$ 
C)  $\{ ( - 3,5 ) \}$ 
D)  $\left\{ \left\{ - \frac { 65 } { 19 } , - \frac { 17 } { 19 } \right) \right\}$

Question 13

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The determinant of a $3 \times 3$ matrix $\mathrm { A } = \left[ \begin{array} { c c c } a _ { 1 } & b _ { 1 } & c _ { 1 } \ a _ { 2 } & b _ { 2 } & c _ { 2 } \ a _ { 3 } & b _ { 3 } & c _ { 3 } \end{array} \right]$ is given by
$$| A | = a _ { 1 } \left| \begin{array} { l } 
\square \square \
\square \square
\end{array} \right| - a _ { 2 } \left| \begin{array} { l } 
\square \square \
\square \square
\end{array} \right| + a _ { 3 } \mid \begin{array} { l } 
\square \square \mid \
\square \square \mid
\end{array}$$

Accepted Answer

\[\left| \begin{array} { l l } 
b _ { 2

Question 14

Determine whether A and B are inverses.
-$$A = \left[ \begin{array} { r r } 
5 & 1 \
- 1 & 2
\end{array} \right] \text { and } B = \left[ \begin{array} { c c } 
\frac { 2 } { 11 } & - \frac { 1 } { 11 } \
\frac { 1 } { 11 } & \frac { 5 } { 11 }
\end{array} \right]$$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-True or false? A system of linear equations in three variables may have no solution.

Accepted Answer

A) True 
 B)False

Question 16

Explain the meaning of the notation $3 \mathrm { R } _ { 1 } + \mathrm { R } _ { 2 } \rightarrow \mathrm { R } _ { 2 }$

Accepted Answer

Add 3 times row 1 to

Question 17

Explain the meaning of $R _ { 1 } \Leftarrow R _ { 3 }$

Accepted Answer

Interchang

Question 18

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { l } 
- 2 x + 5 y + 2 z = - 24 \
x + y - 4 z = 14 \
5 x + 3 y - z = 17
\end{array}$$

Accepted Answer

A)  $\{ ( - 4 , - 2 , - 3 ) \}$ 
B)  $\{ ( - 4 , - 2,3 ) \}$ 
C)  $\{ ( 4 , - 2,3 ) \}$ 
D)  $\{ ( 4 , - 2 , - 3 ) \}$ 
A)  $\{ ( - 4 , - 2 , - 3 ) \}$ 
B)  $\{ ( - 4 , - 2,3 ) \}$ 
C)  $\{ ( 4 , - 2,3 ) \}$ 
D)  $\{ ( 4 , - 2 , - 3 ) \}$

Question 19

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none
of these.
-$$\left[ \begin{array} { c r r } 
4 & - 1 & 2 \
8 & 4 & - 5 \
- 7 & 6 & - 4
\end{array} \right]$$

Accepted Answer

A)  7 , none of these 
B)  9 , square matrix 
C)  $3 \times 3$, square matrix 
D)  $3 \times 3$, none of these 
A)  7 , none of these 
B)  9 , square matrix 
C)  $3 \times 3$, square matrix 
D)  $3 \times 3$, none of these

Question 20

Determine the solution set for the system represented by the augmented matrix.
-$\left[ \begin{array} { r r r | r } 1 & 0 & - 4 & 7 \ 0 & 1 & 8 & - 7 \ 0 & 0 & 0 & 0 \end{array} \right]$

Accepted Answer

A)  $\{ ( 7 - 4 z , - 7 + 8 z , z ) \mid z$ is any real number $\}$ 
B) { } 
C)  $\{ ( 7 , - 7,0 ) \}$ 
D)  $\{ ( 7 + 4 z , - 7 - 8 z , z ) \mid z$ is any real number $\}$ 
A)  $\{ ( 7 - 4 z , - 7 + 8 z , z ) \mid z$ is any real number $\}$ 
B) { } 
C)  $\{ ( 7 , - 7,0 ) \}$ 
D)  $\{ ( 7 + 4 z , - 7 - 8 z , z ) \mid z$ is any real number $\}$

Perform the elementary row operation on the given matrix. - \Leftrightarrow -8 2 -9 -4 -3 7 -6 6 5 0 3 6

Find B - A. - $A = \left[ \begin{array} { r r } 2 & 6 \\4 & 4 \\2 & - 7\end{array} \right] , B = \left[ \begin{array} { r r } - 7 & 6 \\- 5 & - 4 \\7 & 6\end{array} \right]$

Explain the meaning of the notation $- R _ { 2 } \rightarrow R _ { 2 }$

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - $A = \left[ \begin{array} { r r r } - 5 & - 3 & 1 \\- 4 & 3 & - 9 \\- 5 & 6 & 4\end{array} \right]$

Determine whether A and B are inverses. - $A = \left[ \begin{array} { r r r } 0 & 3 & 1 \\1 & - 2 & 0 \\4 & - 1 & 2\end{array} \right] \text { and } B = \left[ \begin{array} { r r r } - 4 & - 7 & 2 \\- 2 & - 4 & 1 \\7 & 12 & - 3\end{array} \right]$

Solve the problem. - a. Write a matrix A that represents the coordinates of the triangle. Place the x-coordinate of each point in the first row of A and the corresponding y-coordinate in the second row of A. b. Use addition of matrices to shift the triangle 5 units to the right and 4 units down.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An $n \times m$ matrix whose elements are all zero is called a ________matrix.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The symbol $I _ { n }$ represents the ________matrix of order n.

Solve the system by using the inverse of the coefficient matrix. - 4x-5y=-11 -2x+3y=5

Given the matrices A and B, solve for X. - $5 X - B = A$ $A = \left[ \begin{array} { r r } - 3 & 5 \\ - 3 & - 4 \end{array} \right]$ and $B = \left[ \begin{array} { l l } - 3 & 4 \\ - 3 & 5 \end{array} \right]$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - x+4y =-7 4x+3y =11

Determine whether A and B are inverses. - $A = \left[ \begin{array} { r r } 5 & 1 \\- 1 & 2\end{array} \right] \text { and } B = \left[ \begin{array} { c c } \frac { 2 } { 11 } & - \frac { 1 } { 11 } \\\frac { 1 } { 11 } & \frac { 5 } { 11 }\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have no solution.

Explain the meaning of the notation $3 \mathrm { R } _ { 1 } + \mathrm { R } _ { 2 } \rightarrow \mathrm { R } _ { 2 }$

Explain the meaning of $R _ { 1 } \Leftarrow R _ { 3 }$

Solve the system by using the inverse of the coefficient matrix. - -2x+5y+2z=-24 x+y-4z=14 5x+3y-z=17

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { c r r } 4 & - 1 & 2 \\8 & 4 & - 5 \\- 7 & 6 & - 4\end{array} \right]$

Determine the solution set for the system represented by the augmented matrix. - $\left[ \begin{array} { r r r | r } 1 & 0 & - 4 & 7 \\ 0 & 1 & 8 & - 7 \\ 0 & 0 & 0 & 0 \end{array} \right]$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 6: Matrices and Determinants and Applications

Perform the elementary row operation on the given matrix. - \Leftrightarrow -8 2 -9 -4 -3 7 -6 6 5 0 3 6

Find B - A. - A=[26442−7],B=[−76−5−476]A = \left[ \begin{array} { r r } 2 & 6 \\4 & 4 \\2 & - 7\end{array} \right] , B = \left[ \begin{array} { r r } - 7 & 6 \\- 5 & - 4 \\7 & 6\end{array} \right]A=​242​64−7​​,B=​−7−57​6−46​​

Explain the meaning of the notation −R2→R2- R _ { 2 } \rightarrow R _ { 2 }−R2​→R2​

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - A=[−5−31−43−9−564]A = \left[ \begin{array} { r r r } - 5 & - 3 & 1 \\- 4 & 3 & - 9 \\- 5 & 6 & 4\end{array} \right]A=​−5−4−5​−336​1−94​​

Solve the problem. - a. Write a matrix A that represents the coordinates of the triangle. Place the x-coordinate of each point in the first row of A and the corresponding y-coordinate in the second row of A. b. Use addition of matrices to shift the triangle 5 units to the right and 4 units down.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An n×mn \times mn×m matrix whose elements are all zero is called a ________matrix.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The symbol InI _ { n }In​ represents the ________matrix of order n.

Solve the system by using the inverse of the coefficient matrix. - 4x-5y=-11 -2x+3y=5

Given the matrices A and B, solve for X. - 5X−B=A5 X - B = A5X−B=A A=[−35−3−4]A = \left[ \begin{array} { r r } - 3 & 5 \\ - 3 & - 4 \end{array} \right]A=[−3−3​5−4​] and B=[−34−35]B = \left[ \begin{array} { l l } - 3 & 4 \\ - 3 & 5 \end{array} \right]B=[−3−3​45​]

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - x+4y =-7 4x+3y =11

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have no solution.

Explain the meaning of the notation 3R1+R2→R23 \mathrm { R } _ { 1 } + \mathrm { R } _ { 2 } \rightarrow \mathrm { R } _ { 2 }3R1​+R2​→R2​

Explain the meaning of R1⇐R3R _ { 1 } \Leftarrow R _ { 3 }R1​⇐R3​

Solve the system by using the inverse of the coefficient matrix. - -2x+5y+2z=-24 x+y-4z=14 5x+3y-z=17

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - [4−1284−5−76−4]\left[ \begin{array} { c r r } 4 & - 1 & 2 \\8 & 4 & - 5 \\- 7 & 6 & - 4\end{array} \right]​48−7​−146​2−5−4​​

Determine the solution set for the system represented by the augmented matrix. - [10−47018−70000]\left[ \begin{array} { r r r | r } 1 & 0 & - 4 & 7 \\ 0 & 1 & 8 & - 7 \\ 0 & 0 & 0 & 0 \end{array} \right]​100​010​−480​7−70​​

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Find B - A. - $A = \left[ \begin{array} { r r } 2 & 6 \\4 & 4 \\2 & - 7\end{array} \right] , B = \left[ \begin{array} { r r } - 7 & 6 \\- 5 & - 4 \\7 & 6\end{array} \right]$

Explain the meaning of the notation $- R _ { 2 } \rightarrow R _ { 2 }$

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - $A = \left[ \begin{array} { r r r } - 5 & - 3 & 1 \\- 4 & 3 & - 9 \\- 5 & 6 & 4\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An $n \times m$ matrix whose elements are all zero is called a ________matrix.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The symbol $I _ { n }$ represents the ________matrix of order n.

Given the matrices A and B, solve for X. - $5 X - B = A$ $A = \left[ \begin{array} { r r } - 3 & 5 \\ - 3 & - 4 \end{array} \right]$ and $B = \left[ \begin{array} { l l } - 3 & 4 \\ - 3 & 5 \end{array} \right]$

Explain the meaning of the notation $3 \mathrm { R } _ { 1 } + \mathrm { R } _ { 2 } \rightarrow \mathrm { R } _ { 2 }$

Explain the meaning of $R _ { 1 } \Leftarrow R _ { 3 }$

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { c r r } 4 & - 1 & 2 \\8 & 4 & - 5 \\- 7 & 6 & - 4\end{array} \right]$

Determine the solution set for the system represented by the augmented matrix. - $\left[ \begin{array} { r r r | r } 1 & 0 & - 4 & 7 \\ 0 & 1 & 8 & - 7 \\ 0 & 0 & 0 & 0 \end{array} \right]$