The symmetric matrix A -428 36 168 (a) Two of the three eigenvalues are 1156 and...

 

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The symmetric matrix A -428 36 168 (a) Two of the three eigenvalues are 1156 and -289. Suppose that the third eigenvalue is k. Enter the value of k in the box below. Number 36 168 367 -792 has three distinct eigenvalues. -792 350 (b) You are given that the symmetric matrix A has three linearly independent eigenvectors with corresponding eigenvalues 1156, -289 and k. Find an orthogonal matrix Q such that D=QT AQ is a diagonal matrix, where 1156 0 0 0 -289 0 0 0 k Enter the matrix Q in the box below. D 12 (0-0) and 8 12 -12 12 -8 -9 The symmetric matrix A -428 36 168 (a) Two of the three eigenvalues are 1156 and -289. Suppose that the third eigenvalue is k. Enter the value of k in the box below. Number 36 168 367 -792 has three distinct eigenvalues. -792 350 (b) You are given that the symmetric matrix A has three linearly independent eigenvectors with corresponding eigenvalues 1156, -289 and k. Find an orthogonal matrix Q such that D=QT AQ is a diagonal matrix, where 1156 0 0 0 -289 0 0 0 k Enter the matrix Q in the box below. D 12 (0-0) and 8 12 -12 12 -8 -9

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