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Unformatted text preview: MAS 3114—Practice Problem Set #2 1. (a) Find the 3 × 3 matrix that produces the transformation “rotate 180 ◦ counterclockwise about the origin” with respect to homogeneous coordinates. (b) Find the 3 × 3 matrix that produces the transformation “rotate 180 ◦ counterclockwise about the point bracketleftbigg 2 3 bracketrightbigg ” with respect to homogeneous coordinates. (c) Let A be an m × n matrix. Define the nullspace of A . 2. Let A = 1 2 2 4 2 1 2 4 . (a) Find a basis for the nullspace of A . (b) Find a basis for the column space of A . (c) Give the LU factorization of A . 3. (a) Define what it means for W to be a subspace of R n . (b) Let A be a 7 × 5 matrix and let vector b ∈ R 5 be a nonzero vector. Is the set { vectorx ∈ R 5 : Avectorx = vector b } a subspace of R 5 ? Give a reason for your answer. 4. (a) Find the 3 × 3 matrix which gives the composite transformation “translate by bracketleftbigg 1 2 bracketrightbigg and then reflect through the...
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This note was uploaded on 12/27/2011 for the course MAS 3114 taught by Professor Olson during the Fall '08 term at University of Florida.
 Fall '08
 Olson

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