Question 1

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

Accepted Answer

A)  $\left[\begin{array}{ll}-6 & 4\end{array}\right]$ 
B)  $\left[\begin{array}{ll}-5 & 4\end{array}\right]$ 
C)  $\left[\begin{array}{ll}0 & 2\end{array}\right]$ 
D)  $\left[\begin{array}{ll}-3 & 4\end{array}\right]$ 
A)  $\left[\begin{array}{ll}-6 & 4\end{array}\right]$ 
B)  $\left[\begin{array}{ll}-5 & 4\end{array}\right]$ 
C)  $\left[\begin{array}{ll}0 & 2\end{array}\right]$ 
D)  $\left[\begin{array}{ll}-3 & 4\end{array}\right]$

Question 2

Use the Gauss-Jordan method to solve the system of equations.
-$x+y+z=9$
$2 x-3 y+4 z=7$
$x-4 y+3 z=-2$

Accepted Answer

A)  $\left(\frac{7 z+34}{5}, \frac{2 z-11}{5}, z\right)$ 
B)  $\left(\frac{-7 z+34}{5}, \frac{2 z+11}{5}, z\right)$ 
C)  $\left(\frac{-7 z+34}{5}, \frac{2 z-11}{5}, z\right)$ 
D)  $\left(\frac{7 z+34}{5}, \frac{2 z+11}{5}, z\right)$ 
A)  $\left(\frac{7 z+34}{5}, \frac{2 z-11}{5}, z\right)$ 
B)  $\left(\frac{-7 z+34}{5}, \frac{2 z+11}{5}, z\right)$ 
C)  $\left(\frac{-7 z+34}{5}, \frac{2 z-11}{5}, z\right)$ 
D)  $\left(\frac{7 z+34}{5}, \frac{2 z+11}{5}, z\right)$

Question 3

Find the inverse, if it exists, of the given matrix.
-$\left[\begin{array}{rrr}1 & 0 & 0 \ -1 & 1 & 0 \ 1 & 1 & 1\end{array}\right]$

Accepted Answer

A) $\left[\begin{array}{rrr}-1 & 0 & 0 \ -1 & -1 & 0 \ -1 & -1 & -1\end{array}\right]$ 
B) $\left[\begin{array}{rrr}1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1\end{array}\right]$ 
C) $\left[\begin{array}{rrr}1 & -1 & 1 \ 0 & 1 & -1 \ 0 & 0 & 1\end{array}\right]$ 
D) $\left[\begin{array}{rrr}1 & 0 & 0 \ 1 & 1 & 0 \ -2 & -1 & 1\end{array}\right]$ 
A) $\left[\begin{array}{rrr}-1 & 0 & 0 \ -1 & -1 & 0 \ -1 & -1 & -1\end{array}\right]$ 
B) $\left[\begin{array}{rrr}1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1\end{array}\right]$ 
C) $\left[\begin{array}{rrr}1 & -1 & 1 \ 0 & 1 & -1 \ 0 & 0 & 1\end{array}\right]$ 
D) $\left[\begin{array}{rrr}1 & 0 & 0 \ 1 & 1 & 0 \ -2 & -1 & 1\end{array}\right]$

Question 4

Solve the problem by writing and solving a suitable system of equations.
-A small business takes out loans from three different banks to buy some new equipment. The total amount of the three loans is $\$ 19,000$. The first bank offered an interest rate of $16 \%$. The second bank offered a rate of $18 \%$ and the amount borrowed from this bank was $\$ 5000$ less than twice as much as the amount borrowed from the first bank. The third bank offered a rate of $15 \%$. The total annual interest was $\$ 3050$. How much did they borrow from each bank?

Accepted Answer

A)  first bank $\$ 6000$, second bank $\$ 7000$, third bank: $\$ 6000$ 
B)  first bank $\$ 5500$, second bank $\$ 6000$, third bank: $\$ 7500$ 
C)  first bank $\$ 5000$, second bank $\$ 5000$, third bank: $\$ 9000$ 
D)  first bank $\$ 4600$, second bank $\$ 4200$, third bank: $\$ 10,200$ 
A)  first bank $\$ 6000$, second bank $\$ 7000$, third bank: $\$ 6000$ 
B)  first bank $\$ 5500$, second bank $\$ 6000$, third bank: $\$ 7500$ 
C)  first bank $\$ 5000$, second bank $\$ 5000$, third bank: $\$ 9000$ 
D)  first bank $\$ 4600$, second bank $\$ 4200$, third bank: $\$ 10,200$

Question 5

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$, whenever the products exist.
-$\mathrm{A}$ is $4 \times 1, \mathrm{~B}$ is $1 \times 4$.

Accepted Answer

A)  $\mathrm{AB}$ is $4 \times 4, \mathrm{BA}$ is $1 \times 1$. 
B)  $\mathrm{AB}$ is $4 \times 4$, $\mathrm{BA}$ is nonexistent. 
C)  $\mathrm{AB}$ is nonexistent, $\mathrm{BA}$ is $1 \mathrm{x} 1$. 
D)  $\mathrm{AB}$ is $1 \times 1$, BA is $4 \times 4$. 
A)  $\mathrm{AB}$ is $4 \times 4, \mathrm{BA}$ is $1 \times 1$. 
B)  $\mathrm{AB}$ is $4 \times 4$, $\mathrm{BA}$ is nonexistent. 
C)  $\mathrm{AB}$ is nonexistent, $\mathrm{BA}$ is $1 \mathrm{x} 1$. 
D)  $\mathrm{AB}$ is $1 \times 1$, BA is $4 \times 4$.

Question 6

The diagram shows the roads connecting four cities.
  How many ways are there to travel between cities $W$ and $Y$ by passing through exactly two cities? (Hint: Write a matrix, A, to represent the number of routes between each pair of cities without passing through another city. Then calculate $\mathrm{A}^{2}$ and $\mathrm{A}^{3}$ ).

Accepted Answer

A)  13 
B)  15 
C)  16 
D)  14 
A)  13 
B)  15 
C)  16 
D)  14

Question 7

What is the size of the matrix?
$\left[\begin{array}{rr}2 & 9 \ -5 & -2\end{array}\right]$

Accepted Answer

A)  1 
B)  2 
C)  $2 \times 2$ 
D)  4 
A)  1 
B)  2 
C)  $2 \times 2$ 
D)  4

Question 8

Determine whether the given ordered set of numbers is a solution of the system of equations.
-$(4,3)$
$3 \mathrm{x}+\mathrm{y}=9$
$2 x+3 y=-1$

Accepted Answer

A) True 
 B)False

Question 9

Determine whether the two matrices are inverses of each other by computing their product.
-$\left[\begin{array}{rr}6 & -5 \ -3 & 5\end{array}\right],\left[\begin{array}{ll}\frac{1}{3} & \frac{1}{3} \ \frac{1}{5} & \frac{2}{5}\end{array}\right]$

Accepted Answer

A) True 
 B)False

Question 10

Given the matrices $A$ and $B$, find the matrix product $A B$.
-$\mathrm{A}=\left[\begin{array}{rr}0 & -2 \ 3 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{rrr}-1 & 3 & 2 \ 0 & -3 & 1\end{array}\right]$ Find $\mathrm{AB}$.

Accepted Answer

A)  $A B$ is not defined. 
B)  $\left[\begin{array}{lll}0 & 6 & -2 \ -3 & 0 & 9\end{array}\right]$ 
C)  $\left[\begin{array}{lll}0 & -3 & 6 \ 0 & -2 & 9\end{array}\right]$ 
D) $\left[\begin{array}{lll}0 & -6 & -4 \ 0 & -9 & 3\end{array}\right]$ 
A)  $A B$ is not defined. 
B)  $\left[\begin{array}{lll}0 & 6 & -2 \ -3 & 0 & 9\end{array}\right]$ 
C)  $\left[\begin{array}{lll}0 & -3 & 6 \ 0 & -2 & 9\end{array}\right]$ 
D) $\left[\begin{array}{lll}0 & -6 & -4 \ 0 & -9 & 3\end{array}\right]$

Question 11

Solve the problem by writing and solving a suitable system of equations.
-Carole's car averages 13.0 miles per gallon in city driving and 21.0 miles per gallon in highway driving. If she drove a total of 443.0 miles on 23 gallons of gas, how many of the gallons were used for city driving?

Accepted Answer

A)  23 gallons 
B)  7 gallons 
C)  18 gallons 
D)  5 gallons 
A)  23 gallons 
B)  7 gallons 
C)  18 gallons 
D)  5 gallons

Question 12

Given the matrices $A$ and $B$, find the matrix product $A B$.
-$\mathrm{A}=\left[\begin{array}{ll}1 & 0 \ 0 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{rrr}5 & 2 & -1 \ 2 & -1 & 2\end{array}\right]$ Find $\mathrm{AB}$.

Accepted Answer

A)  $\mathrm{AB}$ is not defined. 
B) $\left[\begin{array}{lll}5 & 2 & -1 \ 6 & -3 & 6\end{array}\right]$ 
C) $\left[\begin{array}{lll}6 & -3 & 6 \ 5 & 2 & -1\end{array}\right]$ 
D) $\left[\begin{array}{lll}5 & 0 & 0 \ 0 & -3 & 6\end{array}\right]$ 
A)  $\mathrm{AB}$ is not defined. 
B) $\left[\begin{array}{lll}5 & 2 & -1 \ 6 & -3 & 6\end{array}\right]$ 
C) $\left[\begin{array}{lll}6 & -3 & 6 \ 5 & 2 & -1\end{array}\right]$ 
D) $\left[\begin{array}{lll}5 & 0 & 0 \ 0 & -3 & 6\end{array}\right]$

Question 13

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$, whenever the products exist.
-$\mathrm{A}$ is $3 \times 3, \mathrm{~B}$ is $3 \times 3$.

Accepted Answer

A)  $\mathrm{AB}$ is $6 \times 3, \mathrm{BA}$ is $6 \times 3$. 
B)  $\mathrm{AB}$ is $3 \times 3$, $\mathrm{BA}$ is $3 \times 3$. 
C)  $\mathrm{AB}$ is $1 \times 1, \mathrm{BA}$ is $1 \times 1$. 
D)  $\mathrm{AB}$ is $3 \times 6, \mathrm{BA}$ is $3 \times 6$. 
A)  $\mathrm{AB}$ is $6 \times 3, \mathrm{BA}$ is $6 \times 3$. 
B)  $\mathrm{AB}$ is $3 \times 3$, $\mathrm{BA}$ is $3 \times 3$. 
C)  $\mathrm{AB}$ is $1 \times 1, \mathrm{BA}$ is $1 \times 1$. 
D)  $\mathrm{AB}$ is $3 \times 6, \mathrm{BA}$ is $3 \times 6$.

Question 14

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system.
-$\frac{5 x}{2}-\frac{5 y}{4}=-\frac{5}{2}$
$\frac{8 x}{9}=\frac{4}{9}$

Accepted Answer

A)  $\left(\frac{1}{2},-3\right)$ 
B)  $\left(-\frac{1}{2},-3\right)$ 
C)  $\left(-\frac{1}{2}, 3\right)$ 
D)  $\left(\frac{1}{2}, 3\right)$ 
A)  $\left(\frac{1}{2},-3\right)$ 
B)  $\left(-\frac{1}{2},-3\right)$ 
C)  $\left(-\frac{1}{2}, 3\right)$ 
D)  $\left(\frac{1}{2}, 3\right)$

Question 15

Determine whether the two matrices are inverses of each other by computing their product.
-$\left[\begin{array}{ll}9 & 4 \ 4 & 4\end{array}\right],\left[\begin{array}{rr}-.2 & .2 \ .2 & -.45\end{array}\right]$

Accepted Answer

A) True 
 B)False

Question 16

Solve the system by using the inverse of the coefficient matrix.
-$x-y+4 z=-4$
$5 x+z=0$
$x+3 y+z=12$

Accepted Answer

A)  No solution 
B)  $(0,4,-4)$ 
C)  $(0,4,0)$ 
D)  $(0,0,4)$ 
A)  No solution 
B)  $(0,4,-4)$ 
C)  $(0,4,0)$ 
D)  $(0,0,4)$

Question 17

Obtain an equivalent system by performing the stated elementary operation on the system.
-Replace the third equation by the sum of itself and -1 times the second equation.
$x-2 y-7 z=17$
$-6 x+4 y+5 z=-9$
$8 x+7 y-z=-4$

Accepted Answer

A)  $x-2 y-7 z=17$
$14 x+3 y-6 z=5$
$8 x+7 y-z=-4$ 
B)  $x-2 y-7 z=17$
$-6 x+4 y+5 z=-9$
$14 x+3 y-6 z=5$ 
C)  $x-2 y-7 z=17$
$-6 x+4 y+5 z=-9$
$2 x+11 y+4 z=-13$ 
D)  $x-2 y-7 z=17$
$-6 x+4 y+5 z=-9$
$-14 x-3 y+6 z=5$ 
A)  $x-2 y-7 z=17$
$14 x+3 y-6 z=5$
$8 x+7 y-z=-4$ 
B)  $x-2 y-7 z=17$
$-6 x+4 y+5 z=-9$
$14 x+3 y-6 z=5$ 
C)  $x-2 y-7 z=17$
$-6 x+4 y+5 z=-9$
$2 x+11 y+4 z=-13$ 
D)  $x-2 y-7 z=17$
$-6 x+4 y+5 z=-9$
$-14 x-3 y+6 z=5$

Question 18

Obtain an equivalent system by performing the stated elementary operation on the system.
-Interchange equations 1 and 3.
$5 x+5 y+z=7$
$5 x-4 y-z=-33$
$3 x+3 z=1$

Accepted Answer

A)  $3 x \quad+3 z=1$
$5 x-4 y-z=-33$
$5 x+5 y+z=7$ 
B)  $3 x \quad+3 z=1$
$5 x+5 y+z=7$
$5 x-4 y-z=-33$ 
C)  $x+5 y+5 z=7$
$5 x-4 y-z=-33$
$3 x+3 z=1$ 
D)  $5 x-4 y-z=-33$
$5 x+5 y+z=7$
$3 x+3 z=1$ 
A)  $3 x \quad+3 z=1$
$5 x-4 y-z=-33$
$5 x+5 y+z=7$ 
B)  $3 x \quad+3 z=1$
$5 x+5 y+z=7$
$5 x-4 y-z=-33$ 
C)  $x+5 y+5 z=7$
$5 x-4 y-z=-33$
$3 x+3 z=1$ 
D)  $5 x-4 y-z=-33$
$5 x+5 y+z=7$
$3 x+3 z=1$

Question 19

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent.
-$x+y+z=1$
$x-y+5 z=-1$
$4 x+4 y+4 z=10$

Accepted Answer

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

Question 20

The diagram shows the roads connecting four cities.
  How many ways are there to travel between cities $\mathrm{W}$ and $\mathrm{Z}$ by passing through at most one city? (Hint: Write a matrix, A, to represent the number of routes between each pair of cities without passing through another city. Then calculate $\mathrm{A}^{2}$ ).

Accepted Answer

A)  1 
B)  3 
C)  4 
D)  5 
A)  1 
B)  3 
C)  4 
D)  5

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

Use the Gauss-Jordan method to solve the system of equations. - $x+y+z=9$ $2 x-3 y+4 z=7$ $x-4 y+3 z=-2$

Find the inverse, if it exists, of the given matrix. - $\left[\begin{array}{rrr}1 & 0 & 0 \\ -1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]$

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$ , whenever the products exist. - $\mathrm{A}$ is $4 \times 1, \mathrm{~B}$ is $1 \times 4$ .

What is the size of the matrix? $\left[\begin{array}{rr}2 & 9 \\ -5 & -2\end{array}\right]$

Determine whether the given ordered set of numbers is a solution of the system of equations. - $(4,3)$ $3 \mathrm{x}+\mathrm{y}=9$ $2 x+3 y=-1$

Determine whether the two matrices are inverses of each other by computing their product. - $\left[\begin{array}{rr}6 & -5 \\ -3 & 5\end{array}\right],\left[\begin{array}{ll}\frac{1}{3} & \frac{1}{3} \\ \frac{1}{5} & \frac{2}{5}\end{array}\right]$

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $\mathrm{A}=\left[\begin{array}{rr}0 & -2 \\ 3 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{rrr}-1 & 3 & 2 \\ 0 & -3 & 1\end{array}\right]$ Find $\mathrm{AB}$ .

Solve the problem by writing and solving a suitable system of equations. -Carole's car averages 13.0 miles per gallon in city driving and 21.0 miles per gallon in highway driving. If she drove a total of 443.0 miles on 23 gallons of gas, how many of the gallons were used for city driving?

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $\mathrm{A}=\left[\begin{array}{ll}1 & 0 \\ 0 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{rrr}5 & 2 & -1 \\ 2 & -1 & 2\end{array}\right]$ Find $\mathrm{AB}$ .

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$ , whenever the products exist. - $\mathrm{A}$ is $3 \times 3, \mathrm{~B}$ is $3 \times 3$ .

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. - $\frac{5 x}{2}-\frac{5 y}{4}=-\frac{5}{2}$ $\frac{8 x}{9}=\frac{4}{9}$

Determine whether the two matrices are inverses of each other by computing their product. - $\left[\begin{array}{ll}9 & 4 \\ 4 & 4\end{array}\right],\left[\begin{array}{rr}-.2 & .2 \\ .2 & -.45\end{array}\right]$

Solve the system by using the inverse of the coefficient matrix. - $x-y+4 z=-4$ $5 x+z=0$ $x+3 y+z=12$

Obtain an equivalent system by performing the stated elementary operation on the system. -Replace the third equation by the sum of itself and -1 times the second equation. $x-2 y-7 z=17$ $-6 x+4 y+5 z=-9$ $8 x+7 y-z=-4$

Obtain an equivalent system by performing the stated elementary operation on the system. -Interchange equations 1 and 3. $5 x+5 y+z=7$ $5 x-4 y-z=-33$ $3 x+3 z=1$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x+y+z=1$ $x-y+5 z=-1$ $4 x+4 y+4 z=10$

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Mathematics of Finance

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Exam 6: Systems of Linear Equations and Matrices

Perform the indicated operation. -Let A=[−32]A=\left[\begin{array}{ll}-3 & 2\end{array}\right]A=[−3​2​] and B=[10]B=\left[\begin{array}{ll}1 & 0\end{array}\right]B=[1​0​] . Find 2A+3B2 A+3 B2A+3B .

Use the Gauss-Jordan method to solve the system of equations. - x+y+z=9x+y+z=9x+y+z=9 2x−3y+4z=72 x-3 y+4 z=72x−3y+4z=7 x−4y+3z=−2x-4 y+3 z=-2x−4y+3z=−2

Find the inverse, if it exists, of the given matrix. - [100−110111]\left[\begin{array}{rrr}1 & 0 & 0 \\ -1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]​1−11​011​001​​

Find the order of the matrix product AB\mathrm{AB}AB and the product BA\mathrm{BA}BA , whenever the products exist. - A\mathrm{A}A is 4×1, B4 \times 1, \mathrm{~B}4×1, B is 1×41 \times 41×4 .

What is the size of the matrix? [29−5−2]\left[\begin{array}{rr}2 & 9 \\ -5 & -2\end{array}\right][2−5​9−2​]

Determine whether the given ordered set of numbers is a solution of the system of equations. - (4,3)(4,3)(4,3) 3x+y=93 \mathrm{x}+\mathrm{y}=93x+y=9 2x+3y=−12 x+3 y=-12x+3y=−1

Solve the problem by writing and solving a suitable system of equations. -Carole's car averages 13.0 miles per gallon in city driving and 21.0 miles per gallon in highway driving. If she drove a total of 443.0 miles on 23 gallons of gas, how many of the gallons were used for city driving?

Find the order of the matrix product AB\mathrm{AB}AB and the product BA\mathrm{BA}BA , whenever the products exist. - A\mathrm{A}A is 3×3, B3 \times 3, \mathrm{~B}3×3, B is 3×33 \times 33×3 .

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. - 5x2−5y4=−52\frac{5 x}{2}-\frac{5 y}{4}=-\frac{5}{2}25x​−45y​=−25​ 8x9=49\frac{8 x}{9}=\frac{4}{9}98x​=94​

Determine whether the two matrices are inverses of each other by computing their product. - [9444],[−.2.2.2−.45]\left[\begin{array}{ll}9 & 4 \\ 4 & 4\end{array}\right],\left[\begin{array}{rr}-.2 & .2 \\ .2 & -.45\end{array}\right][94​44​],[−.2.2​.2−.45​]

Solve the system by using the inverse of the coefficient matrix. - x−y+4z=−4x-y+4 z=-4x−y+4z=−4 5x+z=05 x+z=05x+z=0 x+3y+z=12x+3 y+z=12x+3y+z=12

Obtain an equivalent system by performing the stated elementary operation on the system. -Interchange equations 1 and 3. 5x+5y+z=75 x+5 y+z=75x+5y+z=7 5x−4y−z=−335 x-4 y-z=-335x−4y−z=−33 3x+3z=13 x+3 z=13x+3z=1

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - x+y+z=1x+y+z=1x+y+z=1 x−y+5z=−1x-y+5 z=-1x−y+5z=−1 4x+4y+4z=104 x+4 y+4 z=104x+4y+4z=10

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Mathematics of Finance

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

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

Use the Gauss-Jordan method to solve the system of equations. - $x+y+z=9$ $2 x-3 y+4 z=7$ $x-4 y+3 z=-2$

Find the inverse, if it exists, of the given matrix. - $\left[\begin{array}{rrr}1 & 0 & 0 \\ -1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]$

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$ , whenever the products exist. - $\mathrm{A}$ is $4 \times 1, \mathrm{~B}$ is $1 \times 4$ .

What is the size of the matrix? $\left[\begin{array}{rr}2 & 9 \\ -5 & -2\end{array}\right]$

Determine whether the given ordered set of numbers is a solution of the system of equations. - $(4,3)$ $3 \mathrm{x}+\mathrm{y}=9$ $2 x+3 y=-1$

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$ , whenever the products exist. - $\mathrm{A}$ is $3 \times 3, \mathrm{~B}$ is $3 \times 3$ .

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. - $\frac{5 x}{2}-\frac{5 y}{4}=-\frac{5}{2}$ $\frac{8 x}{9}=\frac{4}{9}$

Determine whether the two matrices are inverses of each other by computing their product. - $\left[\begin{array}{ll}9 & 4 \\ 4 & 4\end{array}\right],\left[\begin{array}{rr}-.2 & .2 \\ .2 & -.45\end{array}\right]$

Solve the system by using the inverse of the coefficient matrix. - $x-y+4 z=-4$ $5 x+z=0$ $x+3 y+z=12$

Obtain an equivalent system by performing the stated elementary operation on the system. -Interchange equations 1 and 3. $5 x+5 y+z=7$ $5 x-4 y-z=-33$ $3 x+3 z=1$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x+y+z=1$ $x-y+5 z=-1$ $4 x+4 y+4 z=10$