opatovaL

2021-02-25

Find if possible the matrices:
a) AB b) BA.
$A=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right],B=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$

Arnold Odonnell

Step 1
It is given that,
$A=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right],B=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$
We have to find if possible the matrices:
a) AB b) BA.
Step 2
We have , $A=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right],B=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$
a) AB
$⇒AB=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]\cdot \left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$
$⇒AB=\left[\begin{array}{cc}3×0+\left(-2\right)5& 3×0+\left(-2\right)\left(-6\right)\\ 1×0+5×5& 1×0+5\left(-6\right)\end{array}\right]$
$⇒AB=\left[\begin{array}{cc}-10& 12\\ 25& -30\end{array}\right]$
Hence , $AB=\left[\begin{array}{cc}-10& 12\\ 25& -30\end{array}\right]$
b) BA
$⇒BA=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]\cdot \left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$
$⇒BA=\left[\begin{array}{cc}0×3+0×1& 0×\left(-2\right)+0×5\\ 5×3+\left(-6\right)×1& 5×\left(-2\right)+\left(-6\right)×5\end{array}\right]$
$⇒BA=\left[\begin{array}{cc}0& 0\\ 9& -40\end{array}\right]$
Hence , $BA=\left[\begin{array}{cc}0& 0\\ 9& -40\end{array}\right]$

Jeffrey Jordon

Answer is given below (on video)

Jeffrey Jordon