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mid1w06a - A =-2 3-2 1 1 2 1 3-1 1-1(a Find all the source...

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Print Name: Student Number: Section Time: Math 20F. Midterm Exam 1 February 8, 2006 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (10 points) Consider the matrix A and the vector b given by A = - 1 - 2 1 3 2 - 6 1 1 - 2 , b = 2 3 4 . (a) Find the inverse of A . Justify your answer. (b) Find the solution of the non-homogeneous system A x = b . Justify your answer. # Score 1 2 3 4 Σ
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2. (12 points) Consider the matrices A = 1 3 - 2 2 4 - 1 , B = 1 - 1 1 2 . For each of the following expressions, compute it or explain why it is not defined. (a) A 2 and B 3 . (b) ( BA ) T - 2 A T . (c) A - 1 , and B - 1 . (d) Find a 2 × 3 matrix C such that BC = 1 3 1 2 4 - 1 .
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Unformatted text preview: A = -2 3-2 1 1 2 1 3-1 1-1 . (a) Find all the source vectors b such that the non-homogeneous system A x = b is consistent, and write these b in parametric form. Justify your answer. (b) Find the null space of A . Justify your answer. 4. (10 point) Let W be the subspace of IR 4 of vectors of the form W = 2 x + 3 y x + 2 y + z-4 z-2 y , x, y, z ∈ IR . (a) Find a set of vectors in IR 4 whose span is W . Justify your answer. (b) Find a basis for W , that is, a l.i. set of vectors in W that spans W . Justify your answer....
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