Multiply matrices, simplify matrix expressions and solve A + X = B

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Milo has matrix A, which is 2 × 3, and matrix B, which is 3 × 4. What size is AB?

   • 4 × 2
   • 2 × 4
   • 3 × 3
   • Undefined: A and B are different sizes
2. 2.

   For a puzzle, Noah multiplies a 3 × 2 matrix A by a 2 × 5 matrix B. What size is AB?

   • Undefined: A and B are different sizes
   • 5 × 3
   • 2 × 2
   • 3 × 5
3. 3.

   Ren is asked for AB, where A is 2 × 3 and B is 2 × 3. What size is AB?

   • 3 × 2
   • 2 × 3
   • Undefined: A has 3 columns but B has 2 rows
4. 4.

   A is a 3 × 4 matrix and B is a 3 × 2 matrix. What size is AB, the product Tala wants?

   • 3 × 2
   • Undefined: A has 4 columns but B has 3 rows
   • 4 × 3

5. Read this first

   Matrix A

   Row 1: -2, -5, 5; row 2: 5, -3, 5; row 3: -3, 5, -2. Matrix B: row 1: -2, 5; row 2: 6, 4; row 3: 6, -1. Colored: row 3 of A, (-3, 5, -2), and column 1 of B, (-2, 6, 6).

6. 5.

   Jun multiplies row 3 of A by column 1 of B. What is the entry in row 3, column 1 of AB?

   24
7. 6.

   Row 1: -3, 5; row 2: 4, -2. Matrix B: row 1: 2, 2; row 2: -3, 1. Milo finds one entry of the product AB. What is the entry in row 2, column 1?

   14
8. 7.

   Row 1: -2, 1; row 2: 3, 6. Matrix B: row 1: 2, -2; row 2: 1, 3. What is the entry in row 2, column 2 of AB, the product Noah is working on?

   12
9. 8.

   Row 1: -3, 3; row 2: 1, 5. Matrix B: row 1: 6, 5; row 2: -2, 5. Pia checks row 1, column 1 of AB. What is that entry?

   -24
10. 9.

    Row 1: -8, -8; row 2: 1, -5. Matrix B: row 1: 6, 7; row 2: -7, 8. Jun solves the matrix equation A + X = B. What is the entry in row 1, column 2 of X?

    15
11. 10.

    Row 1: 3, -4; row 2: -3, 6. Matrix B: row 1: 1, 9; row 2: 12, 1. In Luz's puzzle, A + X = B. What number goes in row 2, column 2 of X?

    -5