


Solve the following problems, showing any necessary work. 1. [3 points) Find a basis for W+,...
(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.
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(12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
(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-
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(10 points) Find the closest point to y in the subspace W spanned by vì and v2. -4 -2 у 0 -1 0 -1 2 3 1 1 1 1 (10 points) The given set is a basis for a subspace W. Use 0 0 0 the Gram-Schmidt process to produce an orthogonal basis for W.
5 5 8 form an orthogonal basis for W Find an The orthonormal basis of the subspace spanned by the vectors is (Use a comma to separate vectors as needed.) The vectors V, -2 and 12 - -3 3 orthonormal basis for W
3 9. Find the orthogonal projection ofv-1.41 onto the subspace w 1 1 3 spanned by the vectors2
3 9. Find the orthogonal projection ofv-1.41 onto the subspace w 1 1 3 spanned by the vectors2
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.
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
6. Choose one problem, mark it, and solve it. (10 points) Find the closest point to y in the subspace W spanned by v, and v2. (8 points) Is the set of following vectors an orthogonal set of vectors? Justify your answer.
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)