001 2 the null space is necessarily theorthogonal

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Unformatted text preview: {(0, 1, 0, 0), (1, 0, −2, 1)}. 001 2 The null space is necessarily theorthogonal complement of the row space. 11 14 −1 1 −1 3 we get the row reduced echelon form (b) Row reducing the matrix 02 0 7 31 35 ￿ ￿ 1 0 1 1/2 . A basis for the null space of our matrix is then {(−1/2, −7/2, 0, 1), (−1, 0, 1, 0)}. 0 1 0 7/2 −1/2 −1 −7/2 0 . Writing these as columns gives us ourt matrix 0 1 1 0 2) (8 points) a) Find the matrix P that projects vectors ￿ ∈ R3 onto the plane x +2y − z = 0. v b) (8 points) Express the vector (−2, −2, 1) as the sum of a ve...
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This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell University (Engineering School).

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