If \(A = \begin{bmatrix}1&4\\-2&3\end{bmatrix}\) and \(B = \begin{bmatrix}2&-1\\0&5\end{bmatrix}\), then the sum of all the elements of the matrix \(3A - 2B\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6
A scalar multiple multiplies every element:
\( \displaystyle 3A = \begin{bmatrix}3&12\\-6&9\end{bmatrix} \)
\( \displaystyle 2B = \begin{bmatrix}4&-2\\0&10\end{bmatrix} \)
Subtracting the corresponding elements:
\( \displaystyle 3A - 2B = \begin{bmatrix}3 - 4&12 + 2\\-6 - 0&9 - 10\end{bmatrix} = \begin{bmatrix}-1&14\\-6&-1\end{bmatrix} \)
The sum of the elements is
\(-1 + 14 - 6 - 1 = 6\)