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Matrix Multiplication — Easy Worksheet 2
Grade 12 · Whoobee Name: ____________________ Date: __________
Solve each problem. When the answer is a matrix, write one number in each box.
How to solve
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Example
Multiply:
| 0 | 2 | ||
| -1 | -1 |
| 2 | 0 | ||
| -2 | 1 |
Answer:
| -4 | 2 | ||
| 0 | -1 |
| -3 | 3 | ||
| -2 | -3 |
| -1 | -1 | ||
| 2 | 2 |
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: -3 × (-1) + 3 × 2 = 3 + 6 = 9. Row 1 · column 2: -3 × (-1) + 3 × 2 = 3 + 6 = 9. Row 2 · column 1: -2 × (-1) + (-3) × 2 = 2 − 6 = -4. Row 2 · column 2: -2 × (-1) + (-3) × 2 = 2 − 6 = -4. The product is
| 9 | 9 | ||
| -4 | -4 |
✓ Correct!
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: -3 × (-1) + 3 × 2 = 3 + 6 = 9. Row 1 · column 2: -3 × (-1) + 3 × 2 = 3 + 6 = 9. Row 2 · column 1: -2 × (-1) + (-3) × 2 = 2 − 6 = -4. Row 2 · column 2: -2 × (-1) + (-3) × 2 = 2 − 6 = -4. The product is
| 9 | 9 | ||
| -4 | -4 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| 1 | 0 | ||
| 3 | 1 |
| 0 | 2 | ||
| 1 | -1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 1 | 3 | ||
| 1 | 2 |
Not quite. The answer is
💡 Multiply every entry by -2: -2 × 1 = -2, -2 × 3 = -6, -2 × 1 = -2, -2 × 2 = -4. The answer is
| -2 | -6 | ||
| -2 | -4 |
✓ Correct!
Not quite. The answer is
💡 Multiply every entry by -2: -2 × 1 = -2, -2 × 3 = -6, -2 × 1 = -2, -2 × 2 = -4. The answer is
| -2 | -6 | ||
| -2 | -4 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| 1 | -2 | ||
| -2 | 2 |
| 1 | 2 | ||
| -1 | 3 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 2 | -3 | ||
| 3 | -1 |
| 3 | 1 | ||
| -2 | 0 |
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: 2 × 3 + (-3) × (-2) = 6 + 6 = 12. Row 1 · column 2: 2 × 1 + (-3) × 0 = 2 + 0 = 2. Row 2 · column 1: 3 × 3 + (-1) × (-2) = 9 + 2 = 11. Row 2 · column 2: 3 × 1 + (-1) × 0 = 3 + 0 = 3. The product is
| 12 | 2 | ||
| 11 | 3 |
✓ Correct!
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: 2 × 3 + (-3) × (-2) = 6 + 6 = 12. Row 1 · column 2: 2 × 1 + (-3) × 0 = 2 + 0 = 2. Row 2 · column 1: 3 × 3 + (-1) × (-2) = 9 + 2 = 11. Row 2 · column 2: 3 × 1 + (-1) × 0 = 3 + 0 = 3. The product is
| 12 | 2 | ||
| 11 | 3 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| -1 | 0 | ||
| -1 | 2 |
| 0 | 3 | ||
| 3 | -1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| -2 | 3 | ||
| 0 | -3 |
Not quite. The answer is
💡 Multiply every entry by 2: 2 × (-2) = -4, 2 × 3 = 6, 2 × 0 = 0, 2 × (-3) = -6. The answer is
| -4 | 6 | ||
| 0 | -6 |
✓ Correct!
Not quite. The answer is
💡 Multiply every entry by 2: 2 × (-2) = -4, 2 × 3 = 6, 2 × 0 = 0, 2 × (-3) = -6. The answer is
| -4 | 6 | ||
| 0 | -6 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| -2 | 0 | ||
| 3 | -1 |
| 0 | -3 | ||
| 2 | 1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| -1 | -1 | ||
| -1 | 2 |
| 1 | -3 | ||
| 0 | 0 |
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: -1 × 1 + (-1) × 0 = -1 + 0 = -1. Row 1 · column 2: -1 × (-3) + (-1) × 0 = 3 + 0 = 3. Row 2 · column 1: -1 × 1 + 2 × 0 = -1 + 0 = -1. Row 2 · column 2: -1 × (-3) + 2 × 0 = 3 + 0 = 3. The product is
| -1 | 3 | ||
| -1 | 3 |
✓ Correct!
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: -1 × 1 + (-1) × 0 = -1 + 0 = -1. Row 1 · column 2: -1 × (-3) + (-1) × 0 = 3 + 0 = 3. Row 2 · column 1: -1 × 1 + 2 × 0 = -1 + 0 = -1. Row 2 · column 2: -1 × (-3) + 2 × 0 = 3 + 0 = 3. The product is
| -1 | 3 | ||
| -1 | 3 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| 0 | -2 | ||
| 1 | -3 |
| -2 | 3 | ||
| 2 | 3 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 1 | 2 | ||
| -1 | 1 |
Not quite. The answer is
💡 Multiply every entry by -5: -5 × 1 = -5, -5 × 2 = -10, -5 × (-1) = 5, -5 × 1 = -5. The answer is
| -5 | -10 | ||
| 5 | -5 |
✓ Correct!
Not quite. The answer is
💡 Multiply every entry by -5: -5 × 1 = -5, -5 × 2 = -10, -5 × (-1) = 5, -5 × 1 = -5. The answer is
| -5 | -10 | ||
| 5 | -5 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| 2 | 1 | ||
| -1 | 3 |
| 0 | 0 | ||
| 1 | 2 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 3 | 2 | ||
| 2 | 1 |
| -3 | 1 | ||
| -2 | 2 |
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: 3 × (-3) + 2 × (-2) = -9 − 4 = -13. Row 1 · column 2: 3 × 1 + 2 × 2 = 3 + 4 = 7. Row 2 · column 1: 2 × (-3) + 1 × (-2) = -6 − 2 = -8. Row 2 · column 2: 2 × 1 + 1 × 2 = 2 + 2 = 4. The product is
| -13 | 7 | ||
| -8 | 4 |
✓ Correct!
Not quite. The answer is
💡 Each entry is a row of the first matrix times a column of the second: multiply matching numbers and add. Row 1 · column 1: 3 × (-3) + 2 × (-2) = -9 − 4 = -13. Row 1 · column 2: 3 × 1 + 2 × 2 = 3 + 4 = 7. Row 2 · column 1: 2 × (-3) + 1 × (-2) = -6 − 2 = -8. Row 2 · column 2: 2 × 1 + 1 × 2 = 2 + 2 = 4. The product is
| -13 | 7 | ||
| -8 | 4 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| 1 | -3 | ||
| 1 | -1 |
| 1 | -2 | ||
| 1 | -2 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| -1 | -2 | ||
| 0 | 0 |
Not quite. The answer is
💡 Multiply every entry by -3: -3 × (-1) = 3, -3 × (-2) = 6, -3 × 0 = 0, -3 × 0 = 0. The answer is
| 3 | 6 | ||
| 0 | 0 |
✓ Correct!
Not quite. The answer is
💡 Multiply every entry by -3: -3 × (-1) = 3, -3 × (-2) = 6, -3 × 0 = 0, -3 × 0 = 0. The answer is
| 3 | 6 | ||
| 0 | 0 |
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| 0 | 1 | ||
| -3 | 3 |
| 3 | 1 | ||
| 2 | -1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Matrix Multiplication — Easy Worksheet 2
Solve each problem. When the answer is a matrix, write one number in each box.