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Math Help - Matrix Question

  1. #1
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    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}<br />
12  & -8 \\ -8  & 15 <br />
\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
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  2. #2
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    find det(A-\lambda I), equate that with zero and you should be able to find \lambda
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  3. #3
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    what is 'I' suppose to represent?
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  4. #4
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    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.
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  5. #5
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    so what does the diagram given used for?
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  6. #6
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    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
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  7. #7
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    The diagram appears to represent the components of the stress tensor.
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