The matrix has eigenvalues -2 and 1. Find its eigenvectors. The eigenvalue -2 has associated eigenvector The eigenvalue 1/ has associated eigenvector A = 16 30 -9 -17

A diagonalization of the matrix A is given in the form P-¹AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) d₁= = ^₂ = 13 = 1007240 18 1007/N +10 18 18 2 1 4 1 2 5 9 4 4 4 0 0 1 4 4 3 9 1 0 1 -1 1 8 0 -1 has eigenspace span has eigenspace span has eigenspace = 80 0 00 0 0 0 -1 (LF) span (smallest λ-value) (largest λ-value)

is an eigenvector of the matrix 2 What is its eigenvalue? Eigenvalue =

The matrix 4 0 0 A 0 4-8 -4 4 -8] has eigenvalues -4, 0, and 4. Find its eigenvectors. The eigenvalue -4 has associated eigenvector The eigenvalue 0 has associated eigenvector The eigenvalue 4 has associated eigenvector 9.

Find the eigenvalues A1 < A2 < A3 and associated unit eigenvectors ủ1, ü2, ūz of the symmetric matrix 4 -2 -2] A = -2 -2 4 -2 4 -2 The eigenvalue X1 = 2 has associated unit eigenvector ū1 The eigenvalue A2 = has associated unit eigenvector ü2 =

The matrix has eigenvalues −4, 1, and 4. Find its eigenvectors. The eigenvalue −4 has associated eigenvector The eigenvalue 1 has associated eigenvector The eigenvalue 4 has associated eigenvector I A || 4 -6 -3 0 6 5 0 -10 -9 -

Find the eigenvalues and eigenvectors of A = Show that the eigenvectors are orthog- onal.

Find the eigenvalues of the matrix Smaller eigenvalue = Associated eigenvector = Larger eigenvalue = Associated eigenvector = -12 -8 40 24 Note: vectors are entered with "angle brackets", such as or .

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