Question

Using \(A=\begin{bmatrix}-2\\4\\5\end{bmatrix}\) and \(B=\begin{bmatrix}1&3&-6\end{bmatrix}\), which matrix equals \(B'A'\)?

Options

• \(\begin{bmatrix}-2&-6&12\\4&12&-24\\5&15&-30\end{bmatrix}\)

• \(\begin{bmatrix}-2&4&5\\-6&12&15\\12&-24&-30\end{bmatrix}\)

• \(\begin{bmatrix}2&-4&-5\\6&-12&-15\\-12&24&30\end{bmatrix}\)

• \(\begin{bmatrix}1&3&-6\\-2&4&5\end{bmatrix}\)

Answer 1

Here, \(B'=\begin{bmatrix}1\\3\\-6\end{bmatrix}\) and \(A'=\begin{bmatrix}-2&4&5\end{bmatrix}\). Their product is \(\begin{bmatrix}-2&4&5\\-6&12&15\\12&-24&-30\end{bmatrix}\), which equals \((AB)'\).