4. Consider the subspace W 3x-2y -2x + y: x, y eR of R³. x+y (a) Find a basis for W. (b) Find a basis for the orthogonal complement W-.

Q: Which of the following are a basis for the orthogonal complement of the span of (1,-2, -5, 1)7 and…

A: NOTE: Refresh your page if you can't see any equations. . write both vectors in the matrix

Q: 1)Let W CR³ be the subspace generated by the vectors (1, 0, 1)and(1, 1, 0). a )Find the orthogonal…

A: Given W⊂R3 be the subspace generated by the vectors (1,0,1) and (1,1,0). Solution a: Since every…

Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x²,1 + x + 4x²,1 – 7x

A: Consider the polynomials: 1-3x+x2, 1+x+4x2, 1-7x To show that the following polynomials form a basis…

Q: V is a vector space with bases B = (v1, V2, v3) and B' = (w1, w2, w3). The change of basis matrix 1…

A:

Q: Consider the basis B = {(2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Q: 3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?

A: Solution

Q: b Ell С pts] Explain how you know that W is a subspace of R¹. er W = a+b+5c = 0, b+2c=0, a +3c+d=0

A:

Q: Which of the following is a basis for the subspace {:) X y z x = y+z and x, y,z €RC M2x3(R) ? 0 x 0…

A:

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A:

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R² and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Q: Explain how fixing a basis v1, corresponding function in n variables of the form q(x1, · ·· , Xn) =…

A:

Q: Show that the set S= {(-2,-4), (1, 2)} is the basis of R2 or not?

A:

Q: a) Give an example of subspaces U = span(f1, f2, f3) and V = span(g1,92; g3) of RaJa] such that…

A:

Q: Find a basis for the subspace of R° that is spanned by the vectors V1= (1,0,0), v2 = (1, 0, 1), v3 =…

A:

Q: 6. Let V = R³ and F = R. Let W = { (a, b, c) | a+b-2c=0 where a, b, c are in R} It can be shown that…

A:

Q: - {{:) ()(}} (3) 2 B be an ordered basis of the vector space R³. Let the vector v = Find the…

A:

Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

Q: Let W = Span(x₁, x₂) where and let y = -0-0 10 0 -7 1 (a) Find an orthogonal basis of W. (b) Find…

A:

Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1,0,0)T., (2,0, 1,0), and (0, 0, 0, 1) form a…

A: The given set is .Now

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R² and let {x1, x2} be the dual basis of B. Then for…

A:

Q: In each item, you are given a set of vectors S the vectors into the columns of a matrix A rref R of…

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: 3. Let W = ((1,2,3,6), (4,–1,3,6), (5, 1, 6, 12)) %3D W2 = ((1,-1,1,1), (2,-1,4, 5)) %3D be…

A:

Q: 1) We write vectors horizontally for this problem. Let U be the subspace of IRS defined by U =…

A:

Q: Q 3: a) i. Show that W is a subspace of R*. ii. Find a basis for W. Let W = ((a +c, a + b + 2c, a +…

A: According to the policy we are allowed to do only one question with their sub-parts (If any). So I…

Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, 0),…

A:

Q: Let W = span(S) where -3 S = 3 Find a basis for W+, the orthogonal complement of W.

A:

Q: Suposse that {V1, V2, ..., Vp} is a basis for a subspace W, and suppose that v = a1V1+@2V2++a,Vp.…

A: