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Question: for the following state of stress the matrix a is...

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For the following state of stress, the matrix A is given. (a) Determine the principal stresses and their directions. 00 -100 -150 100 -500 200 MPa 150 200 400 Do the following by using the symbolic math software: (b) Construct matrix L such that L-A-λ 1, where λ is an unknown scalar and I is the identity matrix. (c) Find the determinant of L and show that it results in third order polynomials in λ (d) Find the roots of Det (L)-0 and show, numerically, that the sum of the three roots for the characteristic equation for each tensor is equal to the sum of the diagonal components of the corresponding tensor and that the ultiplication of the three roots is equal to the determinant of the corresponding tensor.

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