# hw07 - Math 110—Linear Algebra Fall 2009 Haiman Problem...

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Unformatted text preview: Math 110—Linear Algebra Fall 2009, Haiman Problem Set 7 Due Monday, Oct. 19 at the beginning of lecture. Reminder: Midterm 2 is Friday, Oct. 23, covering material from Problem Sets 1 through 7. The emphasis will be on Problem Sets 4 through 7, but you are responsible for knowing the earlier material as well. 1. For the matrices A and D in Section 3.2, Example 3, find invertible matrices G and F such that D = GAF . 2. Let T : P 4 ( R ) → P 4 ( R ) be the linear transformation defined by T ( f ( x )) = f ( x ) + f (1- x ). (a) Find the matrix of T with respect to the basis of monomials { 1 ,x,x 2 ,x 3 ,x 4 } , and calculate rank( T ). (b) Find a basis of the nullspace N ( T ). 3. Invert the matrix 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 and show your method ( i.e. , don’t just plug it into a computer algebra program)....
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hw07 - Math 110—Linear Algebra Fall 2009 Haiman Problem...

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