c-cl-lina.2011t - Linear Algebra MAS4105 6137 Class-C Prof....

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Unformatted text preview: Linear Algebra MAS4105 6137 Class-C Prof. JLF King 1Nov2011 OYOP: For the 2 Essays: Write your grammatical English sentences on every third line, so that I can easily write between the lines. C1: Defn : A collection C := { W 1 ,..., W 8 } of subspaces is linearly-independent if: . . . Thm: For linear-transformation T : V → V , eigenspaces W 1 ,..., W 8 have ( distinct ) eigenvalues β 1 ,...,β 8 . Prove that D := { W 1 ,..., W 8 } is linearly-independent. C2: Matrix M = A B Z D , where A and D are 5 × 5 and 7 × 7, resp., and Z is 7 × 5. Prove that if a GD ( generalized diagonal ) passes through the B block, then it passes through Z . Short answer, OYOP: C3: A system of 3 linear equations in unknowns x 1 ,...,x 5 reduces to the augmented matrix 5 4 0 0 9 7 0 0 3 0 8 3 0 0 0 2 1 , which is almost in RREF. On your own paper, describe the general solution in this form, " x 1 x 2 x 3 x 4 x 5 # = " ?...
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This note was uploaded on 01/26/2012 for the course MAS 4105 taught by Professor Rudyak during the Fall '09 term at University of Florida.

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