5. Suppose that S is the subspace in R3 spanned by the two vectors aj =...
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...
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
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.
#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)?
(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-
(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...
(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 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)
Find a basis for the subspace of R3 spanned by S. S = {(4, 4, 9), (1, 1, 3), (1, 1, 1)} STEP 1: Find the reduced row-echelon form of the matrix whose rows are the vectors in S. 1 0 0 1 0 0 0 x STEP 2: Determine a basis that spans S. 35E
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V) 0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)