# Math Help - Matrix Question

1. ## 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?

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

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

3. what is 'I' suppose to represent?

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

5. so what does the diagram given used for?

6. 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 $\lambda$

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