opatovaL

2021-01-28

compute the indicated matrices $({I}_{2}-D{)}^{2}$

yunitsiL

Skilled2021-01-29Added 108 answers

Step 1

Matrices:

$D=\left[\begin{array}{cc}0& -3\\ -2& 1\end{array}\right]$

${I}_{2}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$({I}_{2}-D{)}^{2}$

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

$={\left[\begin{array}{cc}1& 3\\ 2& 0\end{array}\right]}^{2}$

Step 2

$=\left[\begin{array}{cc}1& 3\\ 2& 0\end{array}\right]\left[\begin{array}{cc}1& 3\\ 2& 0\end{array}\right]$

$=\left[\begin{array}{cc}1\cdot 1+3\cdot 2& 1\cdot 3\\ 2\cdot 1+0\cdot 2& 2\cdot 3\end{array}\right]$

$=\left[\begin{array}{cc}7& 3\\ 2& 6\end{array}\right]$

This is required answer.

Matrices:

Step 2

This is required answer.

Jeffrey Jordon

Expert2022-01-23Added 2575 answers

Answer is given below (on video)