Question

Given the matrices the product $B^{T}AB$ is _______
$A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 4\\ 6& 2& 1\end{array}\right]$ and $B=\left[\begin{array}{c}2\\ 4\\ -2\end{array}\right]$

• A. -20

Answer 1

The correct option is A -20
$A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 4\\ 6& 2& 1\end{array}\right]$ and $B=\left[\begin{array}{c}2\\ 4\\ -2\end{array}\right]$
$B^{T}AB=\left[\begin{array}{ccc}2& 4& -2\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 4\\ 6& 2& 1\end{array}\right]\left[\begin{array}{c}2\\ 4\\ -2\end{array}\right]$
$=\left[\begin{array}{ccc}-6& 8& 20\end{array}\right]\left[\begin{array}{c}2\\ 4\\ -2\end{array}\right]$
$=-12+32-40=-20$