# 5 a if is an eigenvector of c with eigenvalue 3 nd an

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Unformatted text preview: e a basis for V . 5. (a) If ￿ is an eigenvector of C with eigenvalue 3, ﬁnd an eigenvalue u for the matrix −C 3 + 5C − 8I. (b) Are the polynomials p1 (t) = 1 + 3t + t2 + t4 , p2 (t) = −1 + 3t + 2t2 , p3 (t) = 2 − t2 + t4 linearly independent? (c) In this part, A and B are n × n matrices, with det(A) = 2 and det(B ) = 3. Find the determinant of 3AT B −1 . (d) In this part, w1 , .√. , w4 are orthonormal vectors in R11 . Calculate ￿.￿ ￿12w2 − 10w1 + 50w4 ￿. ￿ ￿ ￿ 6. (a) Here V is the plane x − y + 3z = 0, which is a subspace of R3 . Find an orthonormal basis for V ⊥ . (While you are at it, ﬁnd an orthonormal basis for V .) (b) Here we are working in the space P 1 (0, 1) (i.e. span{1, x}). Find a basis {f1 , f2 }...
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## This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell University (Engineering School).

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