Math54MT1(Teleman)

Math54MT1(Teleman) - A-1 ) = 1 det( A ) 4. Consider the set...

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Practice Midterm 1 February 26th, 2007 GSIs: Michaeel Kazi, Ivan Ventura 1. Let A = 1 2 - 3 2 - 1 1 2 - 3 2 - 1 0 1 1 . Find Col( A ), Nul( A ), Col( A 2 ), Nul( A 2 ). 2. Let B = ±² 1 1 ³² 1 - 1 ³´ and C = ±² 2 3 ³² 1 2 ³´ . Find the change of basis matrix P C→B . 3. For the following determine if the statement is true or false and justify your answer. (a) If A and B are invertible, then so is A + B . (b) If AB is invertible then so is A . (c) If T : R m R n is onto and B = { b 1 ,...,b m } is a basis for R m then T ( b 1 ) ,...,T ( b m ) is a basis for R n . (d) det(
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Unformatted text preview: A-1 ) = 1 det( A ) 4. Consider the set W = { p ( x ) ∈ P 3 | p ( x ) = p (-x ) } (a) Prove, using the definition of a subspace, that W is a subspace of P 3 . (b) Find a linear transformation T such that W = ker( T ) [Hint: note that if p ( x ) = p (-x ) then p ( x )-p (-x ) = 0]. (c) Find the matrix of T . (d) Find a basis for W using your answer to 4c. 1...
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This note was uploaded on 02/10/2010 for the course MATH 54 taught by Professor Chorin during the Fall '08 term at Berkeley.

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