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(1 point) Let W be the subspace of R spanned by the vectors 27 1 and...
(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-
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1 and 4 Find the projection matrix P that projects vectors in R3 onto W
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.
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)
Let W be the subspace of R3 spanned by the vectors ⎡⎣⎢113⎤⎦⎥ and ⎡⎣⎢4615⎤⎦⎥. Find the projection matrix P that projects vectors in R3 onto W.
(1 point) Find the orthogonal projection of onto the subspace W of R* spanned by ņ + 9 and Otac projw() = 1
(12 points) Let vi = 1 and let W be the subspace of R* spanned by V, and v. (a) Convert (V. 2) into an ohonormal basis of W NOTE: If your answer involves square roots, leave them unevaluated. Basis = { (b) Find the projection of b = onto W (c) Find two linearly independent vectors in R* perpendicular to W. Vectors = 1
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
(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() =