Results 1 to 7 of 7

Thread: Matrix Question

  1. #1
    Super Member
    Joined
    Dec 2008
    Posts
    509

    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?



    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jul 2009
    From
    Singapore
    Posts
    338
    find $\displaystyle det(A-\lambda I)$, equate that with zero and you should be able to find $\displaystyle \lambda$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2008
    Posts
    509
    what is 'I' suppose to represent?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jul 2009
    From
    Singapore
    Posts
    338
    $\displaystyle I=\left(\begin{array}{cc}1&0\\0&1\end{array}\right )$
    'I' is the unit matrix, all the elements of the leading diagonal are 1 and all other elements are 0.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2008
    Posts
    509
    so what does the diagram given used for?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Jul 2009
    From
    Singapore
    Posts
    338
    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 $\displaystyle \lambda$
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    May 2010
    From
    Texas
    Posts
    48
    The diagram appears to represent the components of the stress tensor.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix question
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: Jan 26th 2010, 07:50 AM
  2. Matrix Question?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Oct 10th 2009, 06:05 AM
  3. a question on 4x4 matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Aug 6th 2009, 11:06 PM
  4. matrix question
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Dec 5th 2008, 09:46 PM
  5. MATRIX question help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Aug 22nd 2007, 05:42 AM

Search Tags


/mathhelpforum @mathhelpforum