+1 (a) (3 points) Find the projection of -300 onto the span of 0 (b) (3...
for the question, thanks for your help!
2. Let 2 -2 -11 1 3 S1 8 and b -2 -5 7 A= -4 5 2-9 18 Moreover, let A be the 4 x 3 matrix consisting of columns in S (a) (2.5 pt) Find an orthonormal basis for span(S). Also find the projection of b onto span(S) (b) (1.5 pt) Find the QR-decomposition of A. (c) (1 pt) Find the least square solution & such that |A - bl2 is...
2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of w = [1, 2,-1,2]T onto the span of ui-|1,-1, 2, 5]T and u2 [2,1,0,-]. Make sure you are working with an orthonormal basis for u span(u, u2 before you use the usual projection formula.
2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of...
Find the orthogonal projection of y onto Span{u1, uz}. g= 4 ] 2015 ܕ 1 ܕ20 ܕ on? 1 3
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the kernel of the matrix-2 Warning. Make sure you have an orthogonal basis before applying formula (4.42)! ; (d) the subspace orthogonal to a (1,-1,0,1)
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the...
Find the projection of the vector v onto the subspace S. 0 -1 -1 1 S = span V = 0 0 1 1 projs v = JOLI
(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-
Question 1 (10 points) Projection matrix and Normal equation: Consider the vectors v1 = (1, 2, 1), V2 = (2,4, 2), V3 = (0,1,0), and v4 = (3, 7,3). (a) (2 points) Obtain a basis for R3 that includes as many of these vectors as possible. (b) (4 points) Obtain the orthogonal projection matrices onto the plane V = span{v1, v3} and its perpendicular complement V+. (c) (2 points) Use this result to decompose the vector b= (-1,1,1) into a...
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax b. 8 1 -7 1 b- 1-17 a. The orthogonal projection of b onto Col A is b-(Simplify your answer) (Simplify your answer.) b A least-squares solution of Ax-b is x
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax b. 8 1 -7 1 b- 1-17 a. The orthogonal projection of b onto Col...
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1. Consider 3-space with the dot product. Algebraically find the projection of ū onto ü. Plot ü, ō, ūl, and ūl. (a) u = (b) u = * 0 (c) ü = U = 0
22. (a) Find two vectors that span the null space of A 3 -1 2 -4 (b) Use the result of part (a) to find the matrix that projects vectors onto the null space of A. (c) Find two orthogonal vectors that span the null space of A. (d) Use the result of (c) to find the matrix that projects vectors onto the nul space of A. Compare this matrix with the one found in part (a). (e) Find the...