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Unformatted text preview: (b) Find a basis for the null space (also known as the kernel) of A. (c) Find an orthogonal basis for the column space of A. MATH-263 Apri1200B 2 has an eigenvalue ). = 5 + 2i and corresponding 8. (10 marks) Find the eigenvalues and corresponding eigenvectors of the symmetric matrix A"=(2 4) 4 -4 Find an orthogonal matrix P with A = PDpT, and D diagonal. Compute the matrices in the standard basis of orthogonal projection onto each eigenspace. ( 6 -1) 9. (12 marks) The matrix A = 5 4 eigenvector ( 1 ~ 2i ) (a) Write down a bas~, in -vectorform, of real solutions of the system x; =6XI-X2 x~ = 5XI + 4X2 (b) Find functions XI(t) and X2(t) which satisfy the system above as well as the initial conditions Xl (0) = 1, X2(0) = O. (c) How do solutions of the system behave as t -t-00 ?...
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