

11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1...
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) 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 =
(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-
#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)?
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...
5. Suppose that S is the subspace in R3 spanned by the two vectors aj = 1 , a2 = 0 . (a) Find the projection matrix P onto S. (b) Find the projection p of b onto S where ſi b= -1 (c) If b is in S then what is Pb? (d) If b is in St then what is Pb?
(1 point) What is the matrix P-(P) for the projection of a vector b є R3 onto the subspace spanned by the vector a- ? 5 9 Pl 3 1 2 P21 23 - P32 31 What is the projection p of the vector b0onto this subspace? 9 Pl Check your answer for p against the formula for p on page 208 in Strang.
(1 point) What is the matrix P-(P) for the projection of a vector b є R3...
28 -? (1 point) Find the orthogonal projection of 14 onto the subspace V of R3 spanned by 32and y- 7 -2 (Note that the two vectors x and y are orthogonal to each other.) projv(V)-
(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
(1 point) Find the orthogonal projection of 11 onto the subspace W of R4 spanned by 1 2 -2 and *20 -2 projw() =