Q: Given the matrix $$A = \begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix}$$, what is $$-A$$?

$$\begin{bmatrix} -2 & 1 \\ -4 & -3 \end{bmatrix}$$

Q: Which of the following is the correct augmented matrix for the system: $$\begin{cases} x + 2y = 11 \\ x - 4y = 6 \end{cases}$$

$$\begin{bmatrix} 1 & 2 & | & 11 \\ 1 & -4 & | & 6 \end{bmatrix}$$

Q: What is the result of multiplying the matrix $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} by $$the scalar $$3$$?

$$\begin{bmatrix} 3 & 6 \\ 9 & 12 \end{bmatrix}$$

Q: Which of the following is the zero matrix of size $$2 \times 3$$?

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

Q: Which of the following is a column matrix?

$$\begin{bmatrix} a_1$ \\ a_2$ \\ a_3$ \end{bmatrix}$$

Q: Which of the following is the correct matrix subtraction for $$A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 1 \\ 2 & 2 \end{bmatrix}$$?

$$\begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}$$

Question 1

Given the system of equations:

$$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Which of the following ordered pairs is a solution to the system?

Accepted Answer

$$(1, 2)$$

Question 2

Which of the following statements is TRUE about a system of two linear equations in two variables where the lines are parallel?

Accepted Answer

The system has no solution.

Question 3

Consider the system:

$$\begin{cases} x - y = 1 \ 2x + y = 5 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 4

If the augmented matrix for a system of equations is:

$$\begin{bmatrix} 1 & 2 & | & 3 \ 2 & 4 & | & 6 \end{bmatrix}$$

What can you conclude about the system?

Accepted Answer

The system has infinitely many solutions.

Question 5

Which of the following is the correct definition of a row matrix?

Accepted Answer

A matrix with only one row.

Question 6

Given the matrix $$A = \begin{bmatrix} 2 & -1 \ 4 & 3 \end{bmatrix}$$, what is $$-A$$?

Accepted Answer

$$\begin{bmatrix} -2 & 1 \ -4 & -3 \end{bmatrix}$$

Question 7

Which operation is NOT allowed when performing row operations to solve a system using matrices?

Accepted Answer

Multiplying a row by zero.

Question 8

A system of equations is called 'square' if:

Accepted Answer

The number of equations equals the number of variables.

Question 9

Given the system:

$$\begin{cases} 5x - y = 2 \ 2x + 5y = 7 \ -3x - y + 8x = 4 \end{cases}$$

How many variables and equations does this system have?

Accepted Answer

3 variables, 3 equations

Question 10

If two lines have the same slope but different y-intercepts, what is true about their system of equations?

Accepted Answer

The system has no solution.

Question 11

Which of the following is the correct augmented matrix for the system:

$$\begin{cases} x + 2y = 11 \ x - 4y = 6 \end{cases}$$

Accepted Answer

$$\begin{bmatrix} 1 & 2 & | & 11 \ 1 & -4 & | & 6 \end{bmatrix}$$

Question 12

What is the result of multiplying the matrix $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} by $$the scalar $$3$$?

Accepted Answer

$$\begin{bmatrix} 3 & 6 \ 9 & 12 \end{bmatrix}$$

Question 13

Which of the following is NOT a property of a matrix in row-echelon form?

Accepted Answer

The leading entry in any nonzero row is always 1.

Question 14

If a system of equations has infinitely many solutions, what can you say about the relationship between the equations?

Accepted Answer

The equations are dependent.

Question 15

Which of the following is the zero matrix of size $$2 	imes 3$$?

Accepted Answer

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

Question 16

Suppose you are given the system:

$$\begin{cases} x + y = 2 \ x - y = 0 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(1, 1)$$

Question 17

Which of the following is a column matrix?

Accepted Answer

$$\begin{bmatrix} a_1$ \ a_2$ \ a_3$ \end{bmatrix}$$

Question 18

If the system of equations is inconsistent, what does this mean about the solution set?

Accepted Answer

There is no solution.

Question 19

Which of the following is the correct matrix subtraction for $$A = \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 1 \ 2 & 2 \end{bmatrix}$$?

Accepted Answer

$$\begin{bmatrix} 1 & 2 \ 2 & 3 \end{bmatrix}$$

Systems of Linear Equations and Matrices: Study Notes

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