Q: If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 0 \\ 1 & 3 \end{bmatrix}$, what is $A + B$?

$\begin{bmatrix} 3 & 2 \\ 4 & 7 \end{bmatrix}$

Q: Which of the following is a zero matrix?

$\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$

Q: If $A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$, what is $2A$?

$\begin{bmatrix} 4 & 6 \\ 8 & 10 \end{bmatrix}$

Q: Which of the following systems is nonlinear?

$\begin{cases} x^2 + y = 3 \\ x - y = 1 \end{cases}$

Question 1

Which of the following best describes a system of linear equations that has no solution?

Accepted Answer

The system is inconsistent and the equations represent parallel lines.

Question 2

Given the system of equations $\begin{cases} x + y = 2 \ x - y = 0 \end{cases}$, what is the solution?

Accepted Answer

$(1, 1)$

Question 3

Which step is NOT part of the substitution method for solving a system of equations?

Accepted Answer

Multiply both equations by a constant to eliminate a variable.

Question 4

Solve the system using the elimination method: $\begin{cases} 2x + 3y = 7 \ 4x - 3y = 1 \end{cases}$

Accepted Answer

$(2, 1)$

Question 5

A system of equations has infinitely many solutions. Which of the following must be true?

Accepted Answer

The equations are dependent and represent the same line.

Question 6

Given the system $\begin{cases} x + y + z = 6 \ 2x - y + z = 3 \ x + 2y - z = 4 \end{cases}$, what is the value of $z$?

Accepted Answer

$z = 2$

Question 7

What is the size of the augmented matrix for the system $\begin{cases} 2x + 3y = 7 \ 3x - 4y = -12 \end{cases}$?

Accepted Answer

2 rows and 3 columns

Question 8

Find the determinant of the matrix $\begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$.

Accepted Answer

$-2$

Question 9

Which of the following is the correct formula for the determinant of a $3 	imes 3$ matrix $A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33} \end{bmatrix}$?

Accepted Answer

$a_{11}a_{22}a_{33} + a_{12}a_{23}a_{31} + a_{13}a_{21}a_{32} - a_{13}a_{22}a_{31} - a_{11}a_{23}a_{32} - a_{12}a_{21}a_{33}$

Question 10

Cramer's Rule can be used to solve a system of equations only if which condition is met?

Accepted Answer

The determinant of the coefficient matrix is nonzero.

Question 11

Given the system $\begin{cases} 2x + y = 5 \ x - y = 1 \end{cases}$, use Cramer's Rule to find $x$.

Accepted Answer

$x = 3$

Question 12

Which of the following is NOT a property of matrix multiplication?

Accepted Answer

Matrix multiplication is commutative.

Question 13

Suppose $A$ is a $2 	imes 3$ matrix and $B$ is a $3 	imes 4$ matrix. What is the size of the product $AB$?

Accepted Answer

$2 	imes 4$

Question 14

If $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 0 \ 1 & 3 \end{bmatrix}$, what is $A + B$?

Accepted Answer

$\begin{bmatrix} 3 & 2 \ 4 & 7 \end{bmatrix}$

Question 15

Which of the following is a zero matrix?

Accepted Answer

$\begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$

Question 16

If $A = \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$, what is $2A$?

Accepted Answer

$\begin{bmatrix} 4 & 6 \ 8 & 10 \end{bmatrix}$

Question 17

Which of the following systems is nonlinear?

Accepted Answer

$\begin{cases} x^2 + y = 3 \ x - y = 1 \end{cases}$

Question 18

Given the nonlinear system $\begin{cases} x^2 + y^2 = 25 \ y = x + 1 \end{cases}$, which of the following is a solution?

Accepted Answer

$(4, 5)$ and $(-3, -2)$

Chapter 5: Systems of Equations and Matrices – College Algebra Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards