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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).
 Fall '05
 HUI
 Math, Linear Algebra, Algebra

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