Q: Which of the following matrices is the result of adding $$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$ and $$\begin{pmatrix} 4 & 3 \\ 2 & 1 \end{pmatrix}$$?

$$\begin{pmatrix} 5 & 5 \\ 5 & 5 \end{pmatrix}$$

Q: Which of the following is the inverse of $$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$?

$$\begin{pmatrix} -2 & 1 \\ 1.5 & -0.5 \end{pmatrix}$$

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

$$\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}$$

Q: If $$A = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}$$, what is $$A^{-1}$$?

$$\begin{pmatrix} 0.5 & 0 \\ -0.1667 & 0.3333 \end{pmatrix}$$

Question 1

Given the arithmetic sequence where the first term is $$a_1 = 4$ and the common difference is d = 3$, what is the 10th term of the sequence?

Accepted Answer

$$a_{10} = 31$$

Question 2

Which of the following is the sum of the first 20 terms of the arithmetic sequence $$2, 5, 8, 11, \ldots$$?

Accepted Answer

$$S_{20} = 640$$

Question 3

If $$\displaystyle \sum_{k=1}^{n} (2k+1) = 209$$, what is the value of $$n$$?

Accepted Answer

$$n = 14$$

Question 4

Which of the following matrices is the result of adding $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$\begin{pmatrix} 4 & 3 \ 2 & 1 \end{pmatrix}$$?

Accepted Answer

$$\begin{pmatrix} 5 & 5 \ 5 & 5 \end{pmatrix}$$

Question 5

Evaluate $$\displaystyle \sum_{k=1}^{5} (k^2$).$$

Accepted Answer

$$55$$

Question 6

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

Accepted Answer

Question 7

Which of the following is the solution to the system: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 2)$$

Question 8

If $$\displaystyle \sum_{k=1}^{n} k = 45$$, what is the value of $$n$$?

Accepted Answer

$$n = 9$$

Question 9

Which of the following is the determinant of $$\begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}$$?

Accepted Answer

$$7$$

Question 10

A geometric sequence has $$a_1 = 2$ and r = 3$. What is the 5th term?

Accepted Answer

$$162$$

Question 11

If $$\displaystyle \sum_{k=1}^{n} 2k = 100$$, what is the value of $$n$$?

Accepted Answer

$$n = 25$$

Question 12

Which of the following is the inverse of $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$?

Accepted Answer

$$\begin{pmatrix} -2 & 1 \ 1.5 & -0.5 \end{pmatrix}$$

Question 13

If $$\displaystyle \sum_{k=1}^{n} (3k-1) = 80$$, what is the value of $$n$$?

Accepted Answer

$$n = 9$$

Question 14

Which of the following is the sum of the geometric series $$2 + 6 + 18 + 54$$?

Accepted Answer

$$80$$

Question 15

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

Accepted Answer

$$\begin{pmatrix} 2 & 1 \ 4 & 3 \end{pmatrix}$$

Question 16

Which of the following is the solution to the system: $$\begin{cases} 2x + 3y = 13 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (4, 3)$$

Question 17

If $$\displaystyle \sum_{k=1}^{n} k^2$ = 385$$, what is the value of $$n$$?

Accepted Answer

$$n = 10$$

Question 18

Which of the following is the sum of the first 15 terms of the arithmetic sequence $$5, 8, 11, \ldots$$?

Accepted Answer

$$345$$

Question 19

If $$A = \begin{pmatrix} 2 & 0 \ 1 & 3 \end{pmatrix}$$, what is $$A^{-1}$$?

Accepted Answer

$$\begin{pmatrix} 0.5 & 0 \ -0.1667 & 0.3333 \end{pmatrix}$$

Study Notes: Systems of Equations and Matrices in Precalculus

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