I would like some guidance on this question please:
Question:Consider A = $\displaystyle \[
\begin{pmatrix}
2 & -5 \\
3 & 1
\end{pmatrix}
\]$ and let $\displaystyle \[B= A^2 -3A+17I $
Show that B = 0
How do I begin answering a question like this?
I would like some guidance on this question please:
Question:Consider A = $\displaystyle \[
\begin{pmatrix}
2 & -5 \\
3 & 1
\end{pmatrix}
\]$ and let $\displaystyle \[B= A^2 -3A+17I $
Show that B = 0
How do I begin answering a question like this?
I hope you know how to multiply two matrices. Find $\displaystyle A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}$
So, $\displaystyle B=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}^2-3\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}+17\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}$
Hope you can continue.
Ok, I figured it out:
B = $\displaystyle \[
\begin{pmatrix}
2 & -5 \\
3 & 1
\end{pmatrix}
\]$$\displaystyle \[
\begin{pmatrix}
2 & -5 \\
3 & 1
\end{pmatrix}
\]$ - $\displaystyle \[
\begin{pmatrix}
6 & -15 \\
9 & 3
\end{pmatrix}
\]$ + $\displaystyle \[
\begin{pmatrix}
17 & 0 \\
0 & 17
\end{pmatrix}
\]$
= $\displaystyle \[
\begin{pmatrix}
-17 & 0 \\
0 & -17
\end{pmatrix}
\]$$\displaystyle \[
\begin{pmatrix}
17 & 0 \\
0 & 17
\end{pmatrix}
\]$ = 0