Worksheet

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

Grade 11 Math Worksheet - Building Confidence

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

  1. 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
    • 2 × 2
    • 5 × 3
    • 3 × 5

  2. Matrix A is 4 × 1 and matrix B is 1 × 3. Pia wants AB. What size is AB?

    • Undefined: A and B are different sizes
    • 1 × 1
    • 3 × 4
    • 4 × 3

  3. Read this first

    Matrix A

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

  4. Zee colors row 2 of A and column 1 of B. What is the entry in row 2, column 1 of AB?

  5. Matrix A

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

  6. To find one entry of AB, Esme uses row 1 of A and column 2 of B. What is that entry?

  7. Matrix A

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

  8. Kira has colored the row and the column to use. What is the entry in row 2, column 2 of AB?

  9. 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?

  10. 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?

  11. 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?

  12. 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?

  13. Row 1: 9, 5; row 2: -7, -7. Matrix B: row 1: 1, 2; row 2: 11, -8. Kira needs the matrix X with A + X = B. What is the entry in row 2, column 1 of X?

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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. 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
    • 2 × 2
    • 5 × 3
    • 3 × 5

  2. Matrix A is 4 × 1 and matrix B is 1 × 3. Pia wants AB. What size is AB?

    • Undefined: A and B are different sizes
    • 1 × 1
    • 3 × 4
    • 4 × 3

  3. Read this first

    Matrix A

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

  4. Zee colors row 2 of A and column 1 of B. What is the entry in row 2, column 1 of AB?

    7

  5. Matrix A

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

  6. To find one entry of AB, Esme uses row 1 of A and column 2 of B. What is that entry?

    18

  7. Matrix A

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

  8. Kira has colored the row and the column to use. What is the entry in row 2, column 2 of AB?

    21

  9. 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

  10. 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

  11. 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

  12. 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

  13. Row 1: 9, 5; row 2: -7, -7. Matrix B: row 1: 1, 2; row 2: 11, -8. Kira needs the matrix X with A + X = B. What is the entry in row 2, column 1 of X?

    18