practiceprob2

practiceprob2 - B = { ~v 1 ,...,~v n } and C = { ~w 1 ,...,...

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Math 235 Assignment 2 Practice Problems 1. Consider the projection proj ( - 2 , 3) : R 2 R 2 onto the line ~x = t ± - 2 3 ² , t R . Determine a geometrically natural basis B and determine the matrix of the transformation with respect to B . 2. Let U , V , W be finite dimensional vector spaces and let L : V U and M : U W be linear mappings. a) Prove that rank( M L ) rank( M ). b) Prove that rank( M L ) rank( L ). c) Prove that if M is invertible, then rank( M L ) = rank L . 3. Let V and W be finite dimensional vectors spaces with bases
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Unformatted text preview: B = { ~v 1 ,...,~v n } and C = { ~w 1 ,..., ~w m } respectively. Dene T : L M ( m,n ) by T ( L ) = C [ L ] B where L is the vector space of all linear mappings L : V W . Prove that T is a linear mapping. 4. Invent a mapping L : R 2 R 2 and a basis B for R 2 , such that Col([ L ] B ) 6 = Range( L ). Justify your answer....
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This note was uploaded on 11/28/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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