# Matrix Question

• Jul 20th 2010, 09:16 PM
Paymemoney
Matrix Question
Hi
I am having trouble with the following problem:

1) An element of a lamina is subjected to normal and tangential stresses on each of its four sides. The associated stress matrix is

$\begin{bmatrix}
12 & -8 \\ -8 & 15
\end{bmatrix}$
.

Calculate the principal stresses, given that each principal stress, $\lambda$
satisifies det(
$A-\lambda I$)=0

The question also had this diagram which i don't understand what is suppose to represent?

http://img28.imageshack.us/img28/844/diagram1e.png

I started finding the det for A, however what should i do next?

det(A) = 12*15- -8*-8
det(A) = 180-64
det(A) = 116

P.S
• Jul 20th 2010, 09:33 PM
arze
find $det(A-\lambda I)$, equate that with zero and you should be able to find $\lambda$
• Jul 20th 2010, 09:37 PM
Paymemoney
what is 'I' suppose to represent?
• Jul 20th 2010, 10:28 PM
arze
$I=\left(\begin{array}{cc}1&0\\0&1\end{array}\right )$
'I' is the unit matrix, all the elements of the leading diagonal are 1 and all other elements are 0.
• Jul 21st 2010, 12:06 AM
Paymemoney
so what does the diagram given used for?
• Jul 21st 2010, 05:08 AM
arze
its the unit matrix I. $\lambda I=\left(\begin{array}{cc}\lambda &0\\0&\lambda\end{array}\right)$, you should know how to add and subtract matrices. With the result of the subtraction, find the determinant, then equate it with 0 and find $\lambda$
• Jul 21st 2010, 06:44 AM
MattMan
The diagram appears to represent the components of the stress tensor.