Question

Given $A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right],$ then find $2A-B$

Answer 1

Given : $A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$

$2A-B=2\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]-\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$

$=\left[\begin{array}{ccc}2& 4& 6\\ 4& 6& 2\end{array}\right]-\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$

$=\left[\begin{array}{ccc}2-3& 4-(-1)& 6-3\\ 4-(-1)& 6-0& 2-2\end{array}\right]$

$=\left[\begin{array}{ccc}-1& 4+1& 3\\ 4+1& 6& 0\end{array}\right]$

$=\left[\begin{array}{ccc}-1& 5& 3\\ 5& 6& 0\end{array}\right]$