If \(A = \begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix}\) and \(kA = \begin{bmatrix} -6 & 2a \\ b & -8 \end{bmatrix}\), then the value of \(k + a + b\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −2
In scalar multiplication every element of A is multiplied by k:
\( \displaystyle kA = \begin{bmatrix} 3k & -2k \\ k & 4k \end{bmatrix} \)
By equality of matrices, the corresponding elements are equal:
\(3k = -6\), so \(k = -2\)
\(4k = -8\), which agrees with \(k = -2\)
\(2a = -2k = 4\), so \(a = 2\)
\(b = k = -2\)
Hence
\(k + a + b = -2 + 2 - 2 = -2\)