If \(A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix}\) and \(B = \begin{bmatrix} -2 & 3 \\ 5 & -4 \end{bmatrix}\), then the matrix \(A' - 2B\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\begin{bmatrix} 6 & -5 \\ -7 & 4 \end{bmatrix}\)
The transpose A' is obtained by writing the rows of A as columns:
\( \displaystyle A' = \begin{bmatrix} 2 & 1 \\ 3 & -4 \end{bmatrix} \)
Multiplying every element of B by 2:
\( \displaystyle 2B = \begin{bmatrix} -4 & 6 \\ 10 & -8 \end{bmatrix} \)
Subtracting element by element:
\( \displaystyle A' - 2B = \begin{bmatrix} 2 + 4 & 1 - 6 \\ 3 - 10 & -4 + 8 \end{bmatrix} \)
\( \displaystyle = \begin{bmatrix} 6 & -5 \\ -7 & 4 \end{bmatrix} \)