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Matrices
· Examples✏️ Worked Examples — Step by Step
E1
EasyDeterminant of [[3, 1], [2, 4]]:
💡 ad − bc.
👁 Show Solution
3·4 − 1·2 = 12 − 2 = 10. ✅ Answer: 10
✅10
E2
MediumA is 3×4, B is 4×2. Shape of AB:
💡 Inner dims must match; outer dims give result.
👁 Show Solution
A(3×4) × B(4×2): inner 4 = 4 ✓. Result is 3×2. ✅ Answer: 3 × 2
✅3×2
E3
ChallengingInverse of [[2, 0], [0, 4]]:
💡 Diagonal matrix → reciprocal of diagonal.
👁 Show Solution
For diagonal A = diag(2, 4), A⁻¹ = diag(1/2, 1/4) = [[1/2, 0], [0, 1/4]]. ✅ Answer: [[1/2, 0], [0, 1/4]]
✅[[1/2, 0], [0, 1/4]]