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tut_tt2_review

# tut_tt2_review - ~ b = 3-1 2 Find the vector ~x that...

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Math 235 Tutorial: Term Test 2 Review 1: Consider Q ( x 1 , x 2 , x 3 ) = 4 x 1 x 2 + 4 x 1 x 3 + 4 x 2 x 3 . Find the symmetric matrix A that corresponds to Q . Express Q in diagonal form and give the change of variables which brings it into this form. Classify Q . 2: (a) Find an orthogonal basis for the rowspace of A = 1 1 - 1 - 1 3 2 0 1 1 0 1 0 . (b) Find an orthogonal basis for (Null A ) . 3: Let A = 1 0 1 1 0 1 1 2 and let ~ b =
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Unformatted text preview: ~ b = 3-1 2 . Find the vector ~x that minimizes k A~x-~ b k . 4: Let A and B be symmetric n × n matrices whose eigenvalues are all positive. Show that the eigenvalues of A + B are all positive. 5: Prove that if B is any invertible n × n matrix, then A = B T B is positive deﬁnite....
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