Example 1 · level 1
Evaluate the determinant of A = [−3, −2; 2, −2].
Show solution
- |A| = (−3)(−2) − (−2)(2)
- = 6 − (−4) = 10.
Answer: 10
CLASS 12 MATHS · DETERMINANTS
Determinant of a 2 × 2 or 3 × 3 matrix
|a b; c d| = ad − bc. For 3 × 3, expand along a row: a₁₁M₁₁ − a₁₂M₁₂ + a₁₃M₁₃, where each M is a 2 × 2 minor. For an n × n matrix, |kA| = kⁿ|A|.
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Worked examples
Example 2 · level 2
Evaluate the determinant of A = [0, −1, −1; 3, −2, 4; 5, 2, −3] (rows separated by semicolons).
Show solution
- Minors: M₁₁ = −2, M₁₂ = −29, M₁₃ = 16.
- |A| = 0(−2) − (−1)(−29) + (−1)(16) = −45.
Answer: -45
Example 3 · level 3
If the determinant of [x, −4; −5, 4] equals −24, find x.
Show solution
- |A| = 4x − 20 = −24.
- 4x = −4, so x = −1.
Answer: -1