Q: Given matrices $$A = \begin{bmatrix} 9 & -3 \\ 2 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}$$, what is $$3A - 2B$$?

$$\begin{bmatrix} 25 & -5 \\ 6 & 2 \end{bmatrix}$$

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

$$\begin{bmatrix} 2 & -4 \\ 5 & 4 \end{bmatrix}$$

Q: Which of the following is the correct augmented matrix for the system: $$\begin{cases} x + 2y + 1z = 3 \\ y - 4x + 5z = -3 \\ -x - 2y + 7z = 1 \end{cases}$$?

$$\begin{bmatrix} 1 & 2 & 1 & 3 \\ -4 & 1 & 5 & -3 \\ -1 & -2 & 7 & 1 \end{bmatrix}$$

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

$$\begin{bmatrix} 4 & 7 \\ 8 & 15 \end{bmatrix}$$

Q: Which of the following systems is consistent and independent?

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

Q: Which of the following is the correct setup for Cramer's Rule for the system $$\begin{cases} 2x + 3y = 7 \\ 4x - y = 5 \end{cases}$$?

$$D = \begin{vmatrix} 2 & 3 \\ 4 & -1 \end{vmatrix}$$, $$D_x = \begin{vmatrix} 7 & 3 \\ 5 & -1 \end{vmatrix}$$, $$D_y = \begin{vmatrix} 2 & 7 \\ 4 & 5 \end{vmatrix}$$

Question 1

Given points $$P = (-2, -3)$$ and $$Q = (-6, 2)$$, what is the equation of the line passing through these points in point-slope form?

Accepted Answer

$$y + 3 = -\frac{5}{4}(x + 2)$$

Question 2

What is the average rate of change of the function $$f(x) = x^2$ - 2$$ between $$x = 2$$ and $$x = 5$$?

Accepted Answer

$$5$$

Question 3

Given matrices $$A = \begin{bmatrix} 9 & -3 \ 2 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 4 \ 0 & -1 \end{bmatrix}$$, what is $$3A - 2B$$?

Accepted Answer

$$\begin{bmatrix} 25 & -5 \ 6 & 2 \end{bmatrix}$$

Question 4

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

Accepted Answer

$$\begin{bmatrix} 2 & -4 \ 5 & 4 \end{bmatrix}$$

Question 5

Use Cramer's Rule to solve the system: $$\begin{cases} 3x - 2y = 0 \ 5x + 10y = 4 \end{cases}. $$What is the value of $$y$$?

Accepted Answer

$$\frac{3}{10}$$

Question 6

Given the system $$\begin{cases} x - y = 2 \ -2y = 2 \ -2x - 3y = -2 \end{cases}$$, what is the solution for $$y$$?

Accepted Answer

$$-1$$

Question 7

Which of the following is the correct augmented matrix for the system: $$\begin{cases} x + 2y + 1z = 3 \ y - 4x + 5z = -3 \ -x - 2y + 7z = 1 \end{cases}$$?

Accepted Answer

$$\begin{bmatrix} 1 & 2 & 1 & 3 \ -4 & 1 & 5 & -3 \ -1 & -2 & 7 & 1 \end{bmatrix}$$

Question 8

If the determinant of a $$2 	imes 2$$ matrix $$A = \begin{bmatrix} a & b \ c & d \end{bmatrix} is $$zero, what does this imply about the system $$A\vec{x} = \vec{b}$$?

Accepted Answer

The system has either no solution or infinitely many solutions.

Question 9

A chemical reaction is modeled by $$C(t) = 5t^2$ - 2t + 1$$, where $$C is $$the concentration at time $$t. $$What is the average rate of change of $$C$$ from $$t = 1 to$$ $$t = 4$$?

Accepted Answer

$$23$$

Question 10

Given the line $$y = -\frac{5}{4}x - \frac{19}{4}$$, what is its $$y-$$intercept?

Accepted Answer

$$-\frac{19}{4}$$

Question 11

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

Accepted Answer

$$\begin{bmatrix} 4 & 7 \ 8 & 15 \end{bmatrix}$$

Question 12

A population grows according to $$P(t) = 100e$$^{0.03t}$$. What is the average rate of change of P$ from t = 0$ to t = 10$? (Round to the nearest integer.)

Accepted Answer

$$35$$

Question 13

Which of the following systems is consistent and independent?

Accepted Answer

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

Question 14

If $$A = \begin{bmatrix} 2 & 1 \ 0 & 3 \end{bmatrix}$$, what is $$\det(A)$$?

Accepted Answer

$$6$$

Question 15

A medical dosage is modeled by $$D(t) = 4t - t^2$. What is the average rate of change of D$ from t = 1$ to t = 3$?

Accepted Answer

$$-1$$

Question 16

Which of the following is the correct setup for Cramer's Rule for the system $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$?

Accepted Answer

$$D = \begin{vmatrix} 2 & 3 \ 4 & -1 \end{vmatrix}$$, $$D_x = \begin{vmatrix} 7 & 3 \ 5 & -1 \end{vmatrix}$$, $$D_y = \begin{vmatrix} 2 & 7 \ 4 & 5 \end{vmatrix}$$

Precalculus Study Guide: Linear Equations, Matrices, and Systems of Equations

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