<p>If \(A = \begin{bmatrix}-1 & x \\ 4 & 2\end{bmatrix}\), \(B = \begin{bmatrix}x & 1 \\ -1 & 0\end{bmatrix}\) and \(AB = \begin{bmatrix}-6 & -1 \\ 10 & 4\end{bmatrix}\) then the value of \(x\) is</p>
Step-by-Step Solution
Key Concept: Compute AB by multiplying the matrices directly, then match corresponding elements with the given result to form equations in x. The key is recognizing that one element equation will typically be sufficient to determine x uniquely.
<p><strong>Step 1:</strong> Compute the product AB element by element.</p><p>For element (1,1): (-1)(x) + (x)(-1) = -x - x = -2x. This equals -6, so -2x = -6 → x = 3</p><p><strong>Step 2:</strong> Verify x = 3 with other elements. For element (1,2): (-1)(1) + (x)(0) = -1 ✓. For element (2,1): (4)(x) + (2)(-1) = 4x - 2 = 4(3) - 2 = 10 ✓. For element (2,2): (4)(1) + (2)(0) = 4 ✓</p><p><strong>Step 3:</strong> All elements match with x = 3.</p><p>∴ Answer: C (x = 3)</p>
Correct Answer: C