Find the value of k for which the matrix [[2, k], [4, 6]] is singular (non-invertible).
Answer and explanation
Correct answer: D. 3
- Step 1: A singular matrix has determinant zero: det = 0. Step 2. Set up equation: (2 × 6) - (4 × k) = 0 => 12 - 4k = 0. Step 3. Solve: 4k = 12 => k = 3. Answer: 3. Why not the others: 2 gives det = 12 - 8 = 4 ≠ 0; 4 gives det = 12 - 16 = -4 ≠ 0; 6 gives det = 12 - 24 = -12 ≠ 0.
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