
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
$\displaystyle \begin{bmatrix}
12 & 8 \\ 8 & 15
\end{bmatrix}$.
Calculate the principal stresses, given that each principal stress, $\displaystyle \lambda$
satisifies det($\displaystyle A\lambda I$)=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) = 18064
det(A) = 116
P.S

find $\displaystyle det(A\lambda I)$, equate that with zero and you should be able to find $\displaystyle \lambda$

what is 'I' suppose to represent?

$\displaystyle I=\left(\begin{array}{cc}1&0\\0&1\end{array}\right )$
'I' is the unit matrix, all the elements of the leading diagonal are 1 and all other elements are 0.

so what does the diagram given used for?

its the unit matrix I. $\displaystyle \lambda I=\left(\begin{array}{cc}\lambda &0\\0&\lambda\end{array}\right)$, 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 $\displaystyle \lambda$

The diagram appears to represent the components of the stress tensor.