The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order x, and x,. 1 3 1 2 - 7 1 1 The orthogonal basis produced using the Gram-Schmidt process for W is { }. (Use a comma to separate vectors as needed.)

The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. An orthogonal basis for W is. (Type a vector or list of vectors. Use a comma to separate vectors as needed.) 8 89 2 -6 N 00

The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order x, and x2. - 2 - 1 - 7 - 1 The orthogonal basis produced using the Gram-Schmidt process for W is (Use a comma to separate vectors as needed.) 2.

Find the new coordinate vector for the vector x after performing the specified change of basis. Consider two bases B = {b₁, b2} and C = {c₁, c2} for a vector space V such that b₁ = c1 − 4c2 and b2 = 6c1 + 5c2. Suppose x = b₁ + 2b₂. That is, suppose [x] = [₁] - Find [x]c.

Find a basis of the given subspace by deleting linearly dependent vectors. {PHE}} 188) S = span of A basis is

Find a basis of the subspace of R4 that consists of all vectors perpendicular to both Basis: 0 -3 9 and 1 8 8

Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. 11 5 -7 6 110 3 7 1 1 3 6 0 0 5 10 - A = B = 4 4 - 3 18 8 0 0 0 - 4 3 3 9 8 0 0 0 ... A column vector basis for Nul A is { }. (Use a comma to separate vectors as needed.)

The vectors V₁ = basis for W. 1 -8 3 and V₂ = 1 - 1 - 3 form an orthogonal basis for W. Find an orthonormal The orthonormal basis of the subspace spanned by the vectors is (Use a comma to separate vectors as needed.)

6. Let B be the following ordered basis for R?: в %3 {(1,—1), (2, -3)} . Find the coordinate vector of v = (-5,8) with respect to B. 1 2 3 (a) [v]B (b) [v]B (c) [v]B = -3 -3 -2 3 -3 (d) [v]B = (e) [v]B 2

Let V₁ = (1,4,5,6,9), v₂ =(3, 2, 1,4, -1), V3 = (-1,0,-1, -2, -1), V4=(2,3,5,7,8), Find a basis for the orthogonal complement of the subspace of RS spanned by the vectors, V1, V2, V3, and V4. Choose the correct answer from the options below. a,((-1,-1,1,0,0), (-2,-1,0,1,0), (1, -2,0,0,1)) b,((-2,-1,1,0,0), (-2,-1,0, 1,0), (-1, -2,0,0,1)) c,(-1,-1,1,0,0), (-2,3,0,1,0), (-1, -2,0,0,1)) d,(-1,-1,1,0,0), (-2,-1,0,1,0), (-1,-1,0,0,1)).