(1 point) -4 Let L be the line spanned by 0 in R Find a basis of the orthogonal complement L1。L Answer:
(5 points) Let 5 -4 v= 1-3 -3 and let W the subspace of R4 spanned by ū and 7. Find a basis of W?, the orthogonal complement of W in R4.
Problem #8: Find a basis for the orthogonal complement of the subspace of R4 spanned by the following vectors. v1 = (1,-1,4,7), v2 = (2,-1,3,6), v3 = (-1,2,-9, -15) The required basis can be written in the form {(x, y, 1,0), (2,w,0,1)}. Enter the values of x, y, z, and w (in that order) into the answer box below, separated with commas.
4 -5 (1 point) Let L be the line given by the span ofin R3. Find a basis for the orthogonal complement L of L. A basis for L is
(1 point) Let u = 1. VE L . and let W the subspace of R4 spanned by {u, v}. Find a basis for WI. Answer:
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Let v = , u = , and let W the subspace of R4 spanned by v and u. Find a basis of W .
(1 point) Find the orthogonal projection of U = onto the subspace W of R4 spanned by --0-0-1 Uw =
(1 point) Find the orthogonal projection of 11 onto the subspace W of R4 spanned by 1 2 -2 and *20 -2 projw() =
(1 point) Find the orthogonal projection of V = onto the subspace V of R4 spanned by X1 = and X2 = 3/2 projv(v) = -39/2
Let W be the subspace of R4 spanned by the orthogonal vectors 1 0 0 ui , ua : 0 1 Find the orthogonal decomposition of v = ܝܬ ܥ 5 -4 6 with respect to W. -5 p= projw (v) = q= perpw («) =