Practice with full answer key
Point 5 of 5 — Determinants, Matrices and Solving Linear EquationsQuestion bank: 0 questions (0 with pictures)
05 Practice with full answer key
- det [[5, 2], [3, 1]] → 5 − 6 = −1
- det [[1, 0, 2], [3, 1, 0], [0, 4, 1]] → 1(1 − 0) − 0 + 2(12 − 0) = 25
- For which k is [[k, 4], [2, k]] singular? → k² − 8 = 0 → k = ±2√2
- A = [[1, 2], [3, 4]]; find A⁻¹ → det = −2 → [[−2, 1], [1.5, −0.5]]
- If |A| = 3 and |B| = 5, find |AB| and |2A| for 2×2 matrices → 15 and 12
- Solve 3x + y = 9, x − y = −1 by Cramer → D = −4, Dx = −8, Dy = −12 → x = 2, y = 3
- Solve x + 2y + z = 4, 2x − y + 3z = 9, 3x + y − z = 2 → x = 1, y = 1, z = 1
- If AB = I, what is B in terms of A? → B = A⁻¹
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