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 ² and ~v 2 = ±1 ² . For a scalar k , consider the linear transformation T : R 2 → R 2 deﬁned by T ( ~x ) = ± 1 k 0 1 ² ~x. Compute the Bmatrix of T . 1...
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 Spring '08
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 Linear Algebra, Algebra, web site, 1K, course web site

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