Matrices and Matrix Operations: Precalculus Math Test – PDF Download

Question 1: Write a data matrix (2 points)

The table shows game statistics.

1. Write a matrix with one row per player and state its dimensions. (1 point)
2. State the entry in row 2, column 3 and what it means. (1 point)

Question 2: Add and scale matrices (2 points)

Use the matrices below.

1. Find \(A+B\). (1 point)
2. Find \(3A-2B\). (1 point)

Question 3: Solve for unknowns (2 points)

Find \(a\), \(b\) and \(c\).

Question 4: Multiply matrices (3 points)

Use the matrices below.

1. State the dimensions of \(RS\). (1 point)

2. Find \(RS\). (2 points)

Question 5: Order of multiplication (2 points)

Find \(AB\) and \(BA\) for the matrices below, and state whether they are equal.

Question 6: Determinants and invertibility (2 points)

For each matrix, find the determinant and state whether the matrix has an inverse.

Question 7: Find and verify an inverse (3 points)

Use matrix \(M\).

1. Find \(\det M\). (1 point)
2. Find \(M^{-1}\). (1 point)
3. Verify by computing \(MM^{-1}\). (1 point)

Question 8: Smoothie stand revenue (4 points)

Sofia sells small, medium and large smoothies. Matrix \(S\) gives the number sold on Saturday and Sunday. Matrix \(P\) gives the prices in dollars.

1. State the dimensions of \(SP\) and what each entry represents. (1 point)
2. Find \(SP\). (2 points)
3. Find the total revenue for both days. (1 point)

See every chapter on the Precalculus math page.