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Unformatted text preview: b. Find a basis for ker( A ). What is the nullity of A ? c. Find a basis for im( A ). What is the rank of A ? Problem 2. Let A and B be n n matrices. a. Show that ker( A ) ker( B A ). b. How does the rank of A compare to the rank of B A ? Explain using the RankNullity Theorem. Problem 3. Let B = ( ~v 1 ,~v 2 ) be the basis for R 2 in terms of the vectors ~v 1 = 1 and ~v 2 = 1 . For a scalar k , consider the linear transformation T : R 2 R 2 dened by T ( ~x ) = 1 k 0 1 ~x. Compute the Bmatrix of T . 1...
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This note was uploaded on 03/31/2012 for the course MA 351 taught by Professor ?? during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 ??
 Linear Algebra, Algebra

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