# More Matrix Algebra

• Aug 28th 2009, 11:24 PM
juliak
More Matrix Algebra
Given that

M =

1 2
-1 3

find the value(s) of p and q given that M^2 + pM + qI = 0

This is what I did:

M^2 =

-1 8
-4 7

Therefore

p ( 1 2 ) + q ( 1 0 )
...(-1 3 ) .....( 0 1)

=

1 -8
4 -7

I don't know what to do next

(sorry i attempted to use the math bbcode but it got all messed up
• Aug 29th 2009, 12:08 AM
Hello juliak
Quote:

Originally Posted by juliak
Given that

M =

1 2
-1 3

find the value(s) of p and q given that M^2 + pM + qI = 0

This is what I did:

M^2 =

-1 8
-4 7

Therefore

p ( 1 2 ) + q ( 1 0 )
...(-1 3 ) .....( 0 1)

=

1 -8
4 -7

I don't know what to do next

(sorry i attempted to use the math bbcode but it got all messed up

You're quite right so far. What you have is:

$p\begin{pmatrix}1 & 2\\-1 & 3\end{pmatrix}+ q\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix} = \begin{pmatrix}1 & -8\\4 & -7\end{pmatrix}$

Now multiply all the elements in the first matrix by $p$, and those in the second by $q$, and add the resulting matrices:

$\Rightarrow \begin{pmatrix} p + q & 2p\\-p&3p+q\end{pmatrix}=\begin{pmatrix}1 & -8\\4 & -7\end{pmatrix}$

Then compare the elements in corresponding positions to find $p$ and $q$. Start with $2p = -8$ ...