Show that B=0

**sparky** · February 19th 2011, 05:48 AM

I would like some guidance on this question please:

Question:Consider A = $ \begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix} $ and let $\[B= A^2 -3A+17I$
Show that B = 0

How do I begin answering a question like this?

**Sudharaka** · February 19th 2011, 06:09 AM

Originally Posted by sparky

I would like some guidance on this question please:

Question:Consider A = $ \begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix} $ and let $\[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 $A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}$

So, $B=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}^2-3\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}+17\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}$

Hope you can continue.

**sparky** · February 19th 2011, 06:15 AM

Ok, I figured it out:

B = $ \begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix} $ $ \begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix} $ - $ \begin{pmatrix} 6 & -15 \\ 9 & 3 \end{pmatrix} $ + $ \begin{pmatrix} 17 & 0 \\ 0 & 17 \end{pmatrix} $

= $ \begin{pmatrix} -17 & 0 \\ 0 & -17 \end{pmatrix} $ $ \begin{pmatrix} 17 & 0 \\ 0 & 17 \end{pmatrix} $ = 0

**sparky** · February 19th 2011, 06:16 AM

Thanks for your reply and assistance Sudharaka!

Originally Posted by Sudharaka

I hope you know how to multiply two matrices. Find $A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}$

So, $B=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}^2-3\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}+17\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}$

Hope you can continue.

**sparky** · February 19th 2011, 06:18 AM

"One reason a dog is such a lovable creature is his tail wags instead of his tongue."

Yeah, humans can be really cruel and insensitive

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