(5 points) Let 5 -4 v= 1-3 -3 and let W the subspace of R4 spanned...
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 («) =
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Let v = , u = , and let W the subspace of R4 spanned by v and u. Find a basis of W .
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
Find the orthogonal projection of v = |8,-5,-5| onto the
subspace W of R^3 spanned by |7,-6,1| and |0,-5,-30|.
(1 point) Find the orthogonal projection of -5 onto the subspace W of R3 spanned by 7 an 30 projw (V)
3) Let W be a subspace of Rs is spanned by the vectors v1 = (1,3,-1,2,3), 02 = (2,7, -2,5,2), 03 = (1,4,-1,3,-1) (a)( 10 pts.) Find a basis for W. What is the dim(W)? (b)(10 pts.Find a basis for the orthogonal complement W of W. What is the dim(W )? IMPORTANT: 1 This nmiant rancioto of 2 hotinns of different wichte
-4 -2 -5 (1 point) Find the orthogonal projection of ū onto the subspace W spanned by -26 11 -35 -3 -3 2 3 -219 -806 projw(Ū) = -17 -950
(1 point) Let u = 1. VE L . and let W the subspace of R4 spanned by {u, v}. Find a basis for WI. Answer:
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
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.
(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