Solved: The 2 2 real symmetric matrix A has two distinct eigenvalues 1 and 2. (a) If v1
Chapter 7, Problem 21(choose chapter or problem)
The 2 2 real symmetric matrix A has two distinct eigenvalues 1 and 2. (a) If v1 = (a, b) is an eigenvector of A corresponding to the eigenvalue 1, determine an eigenvector corresponding to 2, and hence find an orthogonal matrix S such that ST AS = diag(1,2). (b) Use your result from part (a) to find A. [Your answer will involve 1,2, a, and b.]
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