Let A = [ cc 2 & 1 0 & -2 ], B= [ cc 4 & 1 -3 & -2 ] and C= [ cc -3 & 2 -1 & 4 ] FindA ^2+ AC-5B

Given : A = [ cc 2 & 1 0 & -2 ], B = [ cc 4 & 1 -3 & -2 ] and C = [ ll -3 & 2 -1 & 4 ] Now, A^2= [ cc 2 & 1 0 & -2 ] [ cc 2 & 1 0 & -2 ]= [ ll 4+0 & 2-2 0+0 & 0+4 ]= [ ll 4 & 0 0 & 4 ] 5 B= [ cc 20 & 5 -15 & -10 ] A C= [ cc 2 & 1 0 & -2 ] [ ll -3 & 2 -1 & 4 ] = [ cc -6-1 & 4+4 0+2 & 0-8 ]= [ cc -7 & 8 2 & -8 ] A^2+A C-5 B= [ ll 4 & 0 0 & 4 ]+ [ cc -7 & 8 2 & -8 ]- [ cc 20 & 5 -15 & -10 ] = [ cc 4-7-20 & 0+8-5 0+2+15 & 4-8+10 ] = [ cc -23 & 3 17 & 6 ] .

Let A = [ cc 2 & 1 0 & -2 ], B= [ cc 4 & 1 -3 & -2 ] and C= [ cc …

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Question

Let $A =\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right], B=\left[\begin{array}{cc}4 & 1 \\ -3 & -2\end{array}\right]$ and $C=\left[\begin{array}{cc}-3 & 2 \\ -1 & 4\end{array}\right]$ FindA $^2+ AC-5B$

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Answer

Given : $A =\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right], B =\left[\begin{array}{cc}4 & 1 \\ -3 & -2\end{array}\right]$ and $C =\left[\begin{array}{ll}-3 & 2 \\ -1 & 4\end{array}\right]$
Now, $A^2=\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right]\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right]=\left[\begin{array}{ll}4+0 & 2-2 \\ 0+0 & 0+4\end{array}\right]=\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]$
$5 B=\left[\begin{array}{cc}20 & 5 \\ -15 & -10\end{array}\right]$
$A C=\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right]\left[\begin{array}{ll}-3 & 2 \\ -1 & 4\end{array}\right]$
$=\left[\begin{array}{cc}-6-1 & 4+4 \\ 0+2 & 0-8\end{array}\right]=\left[\begin{array}{cc}-7 & 8 \\ 2 & -8\end{array}\right]$
$\therefore A^2+A C-5 B=\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]+\left[\begin{array}{cc}-7 & 8 \\ 2 & -8\end{array}\right]-\left[\begin{array}{cc}20 & 5 \\ -15 & -10\end{array}\right] $
$ =\left[\begin{array}{cc}4-7-20 & 0+8-5 \\ 0+2+15 & 4-8+10\end{array}\right] $
$=\left[\begin{array}{cc}-23 & 3 \\ 17 & 6\end{array}\right] .$