assign3 - y is a basis for a subspace S of R n then ~x perp...

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Math 136 Assignment 3 Due: Wednesday, Jan 25th 1. Let ~u = 2 1 3 and ~v = 1 - 1 1 . Calculate proj ~v ~u and perp ~v ~u . 2. Let ~u = 1 2 - 3 and ~v = 1 0 1 . Calculate proj ~v ~u and perp ~v ~u . 3. Find the projection of ~v = 1 1 2 onto the plane S = span 1 - 2 1 , - 2 1 - 2 . 4. Let P be the plane in R 3 with vector equation ~x = s 1 0 - 1 + t 2 2 - 1 . Find the projection of ~v = 2 3 1 onto P . 5. Prove that if { ~x, ~
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Unformatted text preview: y } is a basis for a subspace S of R n , then { ~x, perp ~x ~ y } is an orthogonal set which spans S . 6. Prove that the solution set of the system a 11 x 1 + a 12 x 2 + ··· + a 1 n x n = 0 . . . . . . = . . . a m 1 x 1 + a m 2 x 2 + ··· + a mn x n = 0 of m linear equations in n variables is a subspace of R n . 1...
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