# Math Help - Matrix to Quadratic equation Help

1. ## Matrix to Quadratic equation Help

Hi all, this is my first post

Could somebody point in the right direction for solving this question.

I have a 2X2 matrix A
-50 -8
336 54
i am asked to find in terms of m, the expression det(A-mI)
and show it as a quadratic expression
[IMG]file:///C:/Users/IANDUG%7E1/AppData/Local/Temp/moz-screenshot.png[/IMG]
Where do i start? I am probably missing something really obvious

All help appreciated

Ian999

2. Originally Posted by Ian999
Hi all, this is my first post

Could somebody point in the right direction for solving this question.

I have a 2X2 matrix A
-50 -8
336 54
i am asked to find in terms of m, the expression det(A-mI)
and show it as a quadratic expression
[IMG]file:///C:/Users/IANDUG%7E1/AppData/Local/Temp/moz-screenshot.png[/IMG]
Where do i start? I am probably missing something really obvious

All help appreciated

Ian999
What is mI?
$\displaystyle m \left [ \begin{array}{11} 1 & 0 \\ 0 & 1 \end{array} \right ] = \left [ \begin{array}{11} m & 0 \\ 0 & m \end{array} \right ]$

So what would be the matrix A - mI? Now take the determinant.

-Dan

3. Assuming your matrix is $\begin{bmatrix}-50 & -8 \\ 336 & 54 \end{bmatrix}$

Then "det(A- mI)" is the determinant
$\left|\begin{array}{cc}-50- m & -8 \\ 336 & 54- m \end{array}\right|$

Calculate that determinant.

4. ## Thanks

Thanks for the advice guys.