(20) Let W be spanned by (1,1,0)7 and (1,-1,2)T in R3x1 Find the projection matrix from R3x1 onto W (a) (1,1,1)7 in 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-
2. (4) Let W = span{(1,1,1), (-1,1,0)). Let v = (1,-1,2). Find the decomposition v = w; + W2, where we W and W, EW+.
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.
Let T: R3 - R be a linear transformation such that T(1,1,1)= (2,0,-1) T(0,-1,2)=(-3,2,-1) T(1,0,1)= (1,1,0) Find T (2,-1,1). a) (10,0,2) b) (3,-2-1) c)(2,2,2) d) (-3,-2, -3)
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.
(1 point) Let W be the subspace of R spanned by the vectors 27 1 and -7 Find the matrix A of the orthogonal projection onto W. A =
- Find the projection of a=(−2,1,4) onto the line x=(3,3,−1)+t(1,2,−2) - Find the projection vector of a onto the line given in part a).
(1 point) Find the orthogonal projection of 11 onto the subspace W of R4 spanned by 1 2 -2 and *20 -2 projw() =
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. b) Find the least squares approximation, £, to the solution vector x of Ai- c) The least squares error is defined to be the length of the vector b - AX. Find this vector and its length. d) What is the relationship between A, , and p? 4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto...
What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p of the vector b-5 onto this subspace? Pi P2 Ps What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p...