Construct a symmetric matrix A by setting A = round(5 rand(6)); A = A + A_ Compute the

Chapter 6, Problem 10

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Construct a symmetric matrix A by setting A = round(5 rand(6)); A = A + A_ Compute the eigenvalues of A by setting e = eig(A). (a) The trace of A can be computed with the MATLAB command trace(A), and the sum of the eigenvalues of A can be computed with the command sum(e). Compute both of these quantities and compare the results. Use the command prod(e) to compute the product of the eigenvalues of A and compare the result with det(A). (b) Compute the eigenvectors of A by setting [X, D] = eig(A). Use MATLAB to compute X1AX and compare the result with D. Compute also A1 and XD1X1 and compare the results. 1

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