lingalghw4 - b pick a basis of V and describe the...

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1 homework 4, due wednesday, 5/4 in class, or in Vladimir’s box by 4:00pm 1.axler chapter 1 numbers 1 , 2, chapter 3 number 11, and chapter 5 number 1. 2. Let V C 3 be the subspace V = { ( x, y, z ) x + y + z = 0 } . Let T : C 3 C 3 be the operator T ( x, y, z ) = ( y, z, x ) . a. show that V is an invariant subspaces.
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Unformatted text preview: b. pick a basis of V , and describe the restriction T | V in that basis. c. find a basis of V in which the matrix, A , of T is diagonal, and write down the ma-trix. d. find a closed formula for A n for all n . 1...
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