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Unformatted text preview: 2 satisﬁes L (1 , 2 , 1) T = (1 , 3) T , L (2 , 1 ,3) T = (1 , 2) T . Is this enough information to ﬁnd L (4 , 5 ,1) T ? If YES, ﬁnd it; if NO, explain why it is impossible. Q10. Find eigenvalues and eigenvectors for the matrix A = ± 3 1 1 3 ² . Q11. With A as in Q10, solve Y = AY, Y (0) = (2 , 6) T . Q12. Find the cube root of A = ±614 7 15 ² . Q13. Find the scalar and vector projections of (1 , 2) T onto (1 , 3) T . Q14. Let { x 1 ,x 2 ,x 3 } be nonzero orthogonal vectors in R 3 . Prove that they are linearly independent. Q15. Let S be the span of (1 , 1 , 1) T and (1 , 2 , 3) T . Find S ⊥ . 2...
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 Fall '08
 boas
 Linear Algebra, Algebra, Matrices, Vector Space, matrix equation XA

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