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Inverse Matrices & Cramer's Rule — Easy Worksheet 1
Grade 12 · MathSheets Name: ____________________ Date: __________
Solve each problem. For a matrix answer, write one number in each box. Write solutions of systems as (x, y).
How to solve
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Example
Find the inverse of
| 3 | 2 | ||
| -1 | -1 |
Answer:
| 1 | 2 | ||
| -1 | -3 |
| 1 | 1 | ||
| -2 | -3 |
Not quite. The answer is
💡 First the determinant: det = ad − bc = 1 × (-3) − 1 × (-2) = -3 − (-2) = -1. Swap a and d and change the signs of b and c:
| -3 | -1 | ||
| 2 | 1 |
| 3 | 1 | ||
| -2 | -1 |
✓ Correct!
Not quite. The answer is
💡 First the determinant: det = ad − bc = 1 × (-3) − 1 × (-2) = -3 − (-2) = -1. Swap a and d and change the signs of b and c:
| -3 | -1 | ||
| 2 | 1 |
| 3 | 1 | ||
| -2 | -1 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| 1 | -4 | ||
| -2 | 7 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 D = det
| -1 | -4 | ||
| -4 | 3 |
| -1 | 2 | ||
| -4 | 27 |
✓ Correct!
Not quite. The answer is
💡 D = det
| -1 | -4 | ||
| -4 | 3 |
| -1 | 2 | ||
| -4 | 27 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| -1 | 3 | ||
| 2 | -5 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 1 | 4 | ||
| -2 | -7 |
Not quite. The answer is
💡 First the determinant: det = ad − bc = 1 × (-7) − 4 × (-2) = -7 − (-8) = 1. Swap a and d and change the signs of b and c:
| -7 | -4 | ||
| 2 | 1 |
| -7 | -4 | ||
| 2 | 1 |
✓ Correct!
Not quite. The answer is
💡 First the determinant: det = ad − bc = 1 × (-7) − 4 × (-2) = -7 − (-8) = 1. Swap a and d and change the signs of b and c:
| -7 | -4 | ||
| 2 | 1 |
| -7 | -4 | ||
| 2 | 1 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| 1 | 1 | ||
| -1 | 0 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 D = det
| 3 | 4 | ||
| -4 | 3 |
| -4 | 4 | ||
| 22 | 3 |
✓ Correct!
Not quite. The answer is
💡 D = det
| 3 | 4 | ||
| -4 | 3 |
| -4 | 4 | ||
| 22 | 3 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| -1 | 0 | ||
| 1 | 1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 4 | 3 | ||
| 1 | 1 |
Not quite. The answer is
💡 First the determinant: det = ad − bc = 4 × 1 − 3 × 1 = 4 − 3 = 1. Swap a and d and change the signs of b and c:
| 1 | -3 | ||
| -1 | 4 |
| 1 | -3 | ||
| -1 | 4 |
✓ Correct!
Not quite. The answer is
💡 First the determinant: det = ad − bc = 4 × 1 − 3 × 1 = 4 − 3 = 1. Swap a and d and change the signs of b and c:
| 1 | -3 | ||
| -1 | 4 |
| 1 | -3 | ||
| -1 | 4 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| 1 | 3 | ||
| 0 | 1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 D = det
| -1 | -2 | ||
| 3 | 3 |
| 4 | -2 | ||
| -6 | 3 |
✓ Correct!
Not quite. The answer is
💡 D = det
| -1 | -2 | ||
| 3 | 3 |
| 4 | -2 | ||
| -6 | 3 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| 3 | 4 | ||
| -1 | -1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 3 | -1 | ||
| 1 | 0 |
Not quite. The answer is
💡 First the determinant: det = ad − bc = 3 × 0 − (-1) × 1 = 0 − (-1) = 1. Swap a and d and change the signs of b and c:
| 0 | 1 | ||
| -1 | 3 |
| 0 | 1 | ||
| -1 | 3 |
✓ Correct!
Not quite. The answer is
💡 First the determinant: det = ad − bc = 3 × 0 − (-1) × 1 = 0 − (-1) = 1. Swap a and d and change the signs of b and c:
| 0 | 1 | ||
| -1 | 3 |
| 0 | 1 | ||
| -1 | 3 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| 1 | -1 | ||
| -2 | 1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Put the constants 21 and -2 in place of the x-coefficients: Dx = det
| 21 | -3 | ||
| -2 | 1 |
✓ Correct!
Not quite. The answer is
💡 Put the constants 21 and -2 in place of the x-coefficients: Dx = det
| 21 | -3 | ||
| -2 | 1 |
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| -1 | 1 | ||
| -1 | 0 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Inverse Matrices & Cramer's Rule — Easy Worksheet 1
Solve each problem. For a matrix answer, write one number in each box. Write solutions of systems as (x, y).