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Unformatted text preview: A . 3 of 7 3. Consider the susbpace W = span { (1 , 3 , 1 ,1) , (2 , 6 , , 1) } of R 4 . Find an orthonormal basis for W ⊥ (the orthogonal complement of W ). 4 of 7 4. Find a basis for, and state the dimension of the subspace W = { A ∈ M 22  A ± 1 11 0 ² = ± 11 1 ² A } of M 22 . 5 of 7 5. Find a basis for P 3 ( R ) that contains the polynomials x 32 x 2 +1 and 2 x 3 +4 x 2x +3. Justify your answer. 6 of 7 6. Let A be an m × n matrix and let W be the nullspace of A . Prove that for all X ∈ R n , AX = A ( proj W ⊥ ( X )) . where proj W ⊥ ( X ) denotes the orthogonal projection of X onto W ⊥ . 7 of 7...
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This note was uploaded on 04/09/2012 for the course MATH 223 taught by Professor P during the Spring '11 term at University of Toronto.
 Spring '11
 p
 Linear Algebra, Algebra

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