If \(A = \begin{bmatrix}2&5&-1\\3&0&4\\1&-2&6\end{bmatrix}\) and \(X = \begin{bmatrix}0\\1\\0\end{bmatrix}\), then AX is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\begin{bmatrix}5\\0\\-2\end{bmatrix}\)
A is of order \(3 \times 3\) and X of order \(3 \times 1\), so AX is a column matrix of order \(3 \times 1\). Multiplying each row of A by X:
\(2(0) + 5(1) + (-1)(0) = 5\)
\(3(0) + 0(1) + 4(0) = 0\)
\(1(0) + (-2)(1) + 6(0) = -2\)
So AX is the second column of A:
\( \displaystyle AX = \begin{bmatrix}5\\0\\-2\end{bmatrix} \)