Matrix Multiplication and What It Represents · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Multiplying matrices in the right order

Mathematics · Linear Algebra · ages 18-19
Name ______________________   Date ____________

  1. A has rows (1, 2) and (3, 4), and B has rows (5, 6) and (7, 8). What is the top left entry of AB?

    Answer: ______________

  2. With A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is the bottom right entry of AB?

    Answer: ______________

  3. With A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is the top left entry of AB?

    Answer: ______________

  4. A is 2 by 3 and B is 3 by 4. What shape is the product AB?

    • 2 by 4
    • 3 by 3
    • 3 by 4

  5. A is a 2 by 2 matrix and v holds 2 entries. How is the product Av best read?

    • A combination of the rows of A
    • One number from the diagonal
    • A combination of the columns of A

  6. A has rows (1, 2) and (3, 4), and B has rows (5, 6) and (7, 8). What is the bottom right entry of AB?

    Answer: ______________

  7. A is a 2 by 2 matrix and v is a vector with 2 entries. How is the product Av best read?

    • A combination of the columns of A
    • A combination of the rows of B
    • The product of the diagonal entries
    • A 2 by 2 matrix

  8. A is a 3 by 2 matrix. Which product with A on the left is defined?

    • A times a 3 by 5 matrix
    • A times a 2 by 5 matrix
    • A times a 5 by 2 matrix

  9. A has rows (1, 2) and (3, 4), and B has rows (5, 6) and (7, 8). What is the top left entry of BA?

    • 23
    • 19
    • 21

  10. A has columns (2, 0) and (0, 2), and v holds entries 3 then 4. What is the top entry of Av?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Multiplying matrices in the right order W1-mt_0fJOMPlCxr-s1

  1. 19 · Pair row 1 of A with column 1 of B: 1 times 5 plus 2 times 7 is 19.
  2. 50 · Row 2 of A dot column 2 of B: 3*6 + 4*8 = 50.
  3. 19 · Row 1 of A dot column 1 of B: 1*5 + 2*7 = 19.
  4. 2 by 4 · The inner sizes agree at 3, so the outer pair gives 2 by 4.
  5. A combination of the columns of A · Each entry of v scales one column of A, and the scaled columns add to Av.
  6. 50 · Pair row 2 of A with column 2 of B: 3 times 6 plus 4 times 8 is 50.
  7. A combination of the columns of A · Av weights each column of A by the matching entry of v.
  8. A times a 2 by 5 matrix · A has 2 columns, so the partner must bring 2 rows: only the 2 by 5 partner fits.
  9. 23 · BA pairs row 1 of B with column 1 of A: 5 times 1 plus 6 times 3 is 23.
  10. 6 · Weight the columns: 3 times (2, 0) plus 4 times (0, 2) is (6, 8).
Worksheet · LightMySky