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Unformatted text preview: T p 1 1 P = 2 3 4 and T p 12 P = 22 3 Find the matrix of T . 4. (10 points) (a) Find the matrix P for projection in R 3 onto the plane 2 x + y + 3 z = 0. (b) Find a nonzero 3 3 matrix B so that BP = 0. 5. (10 points) (a) Let v b be a nonzero vector and suppose that the system Avx = v b has at least 2 diferent solutions. Then show that the homogeneous linear system Avx = v 0 has at least one nonzero solution. (b) IF v b = vV 1 + 2 vV 2 and For A = [ vV 1  vV 2  vV 3 ] we have rreF A = 1 01 0 13 0 0 then nd all solutions to Avx = v b . (c) (True or alse IF true, explain why. IF False, give a counterexample.) IF an n n matrix A is invertible and A 2 = A , then A = I ....
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This note was uploaded on 04/28/2008 for the course MAT 202 taught by Professor Staff during the Spring '08 term at Princeton.
 Spring '08
 Staff
 Math, Linear Algebra, Algebra

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