i need help please in linear algebra 4 (20 pts ah (5 pts) Let N o be a vector in

Question

i need help please in linear algebra

4 (20 pts ah (5 pts) Let N o be a vector in R How many eigenvalues of A- xx are (Hint what is the rank b) (5 pts) suppose that A is a square n x n matrix, ust five statements about Athat are equivalernt to A c) (5 pts) consider the following matrix: Under what conditions on z and y would A be positive semidefinite? d (5 pts) Consider the square matrix i. Pick r so that the Eigen ectors of A can be chosen to be orthogonal v ii, Find and verify that, for the chosen x, the Eigen vectors are indeed orthogonal

Explanation / Answer

Ans(a):

Since A is symmetric positive semidenite with rank 1, then there are 1 positive, 2 zero, and no negative eigenvalues.

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