0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero...
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.
#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) Determine if w is in the subspace spanned by v1, v2, v3 2) Are the vectors v1, v2, v3 linearly dependent or independent? justify your answer Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
Let U be a square matrix with orthonormal columns. Which of the following is true of the columns of U? They are the same as the rows of U. The inner product of each pair of column vectors is 0. Each column vector has unit length. They are linearly independent B, C, D are correct. A, C, D are correct. All A, B, C, D are correct. Next Previous Let U be a square matrix with orthonormal columns. Which of...
Let W be the subspace of R4 spanned by the orthogonal vectors 1 0 0 ui , ua : 0 1 Find the orthogonal decomposition of v = ܝܬ ܥ 5 -4 6 with respect to W. -5 p= projw (v) = q= perpw («) =
(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
Question 6 10 pts What is the dimension of the subspace of M22 (R) spanned by the set of 4 vectors şfi 01.1 110 1111 -21} IO 1]'1 0 LO 11-1 1 JS
ote: The norm of is denoted by |vand is calculated N a vector u Consider a subspace W of R4, W span(1, v2, v3, v4)). Where 0 из- 1. Find an orthonormal basis Qw of W and find the dimension of W 2. Find an orthonormal basis QWL of WL and find the dimension of WL 3. GIven a vector u- . find the Qw coordinate of Projw(v) . find the Qwa coordinate of Projwi (v) » find the coordinate...
All vectors and subspaces are in R”. Mark each statement True or False. Justify each answer. Complete parts (a) through (e) below. a. If W is a subspace of R" and if y is in both W and wt, then y must be the zero vector. If v is in W, then projwv = Since the wt component of v is equal to v the w+ component of v must be A similar argument can be formed for the W...
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...