Matrices Test – Precalculus Math (Printable PDF)

Question 1 Combining Matrices (2 points)

Let A have rows (3, −1) and (0, 4), and B have rows (2, 5) and (−3, 1). Find 2A − B.

Question 2 A 2 × 2 Product (2 points)

Find AB, where A has rows (4, −2) and (1, 3), and B has rows (−1, 5) and (2, 0).

Question 3 Sizes of Products (2 points)

Suppose A has size 3 × 2, B has size 2 × 5 and C has size 3 × 5.

1. Can AB be formed? If so, state its size. (1 point)
2. Can BA be formed? Can A + C be formed? Explain. (1 point)

Question 4 Determinants (2 points)

(a) Compute the determinant of the matrix with rows (−3, 7) and (2, 5). (1 point)

(b) Determine every k that makes the matrix with rows (k, 9) and (4, k) singular. (1 point)

Question 5 An Inverse Matrix (3 points)

Let A have rows (2, 4) and (3, 5).

1. Find det A. (1 point)
2. Find A⁻¹. (1 point)
3. Verify your answer by showing that AA⁻¹ = I. (1 point)

Question 6 A Row of a 3 × 3 Product (3 points)

Let A have rows (2, 0, 1), (1, 3, −2) and (0, 4, 1), and B have rows (1, −1, 2), (0, 2, 3) and (3, 1, −1). Find the second row of AB.

Question 7 School Store Revenue (3 points)

A school store sells notebooks at $3.00, pens at $1.25 and folders at $2.00. The figure shows what it sold in two semesters.

1. Write the sales as a 2 × 3 matrix and the prices as a 3 × 1 matrix. (1 point)
2. Find the product that gives the revenue for each semester. (1 point)
3. State which semester earned more and by how much. (1 point)

Question 8 Products and Determinants (3 points)

Let A have rows (2, 0) and (1, 3), and B have rows (1, 4) and (−2, 1).

1. Find AB. (1 point)
2. Find BA. Is AB = BA? (1 point)
3. Find det(AB), det A and det B. What do you notice? (1 point)