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: 4. Use the 3-space standard basis vectors to find three nonzero vectors a, b, c satisfying axb = a x…

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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: 2b Let W = { "] | a, b e R}. a. Find a basis for W. (Your work here proves that W is a subspace of…

A: Given below the detailed solution

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: 14. Let P₂ be the vector space of polynomials of degree ≤ 2. Let D = {1 + t, 1 − 5t, 2 + t²}. Check…

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Q: Let W= span{(1,2,-1,0),(2,2,0,1),(1,1,-1,0)}. Use Gram Schmidt to find an orthogonal basis for W.

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

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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: 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

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

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Q: 5. Consider the space {) a a + b+c= d : 2a + b = d a + b+ 3c = 0 H = CRª. C d (a) Find a matrix A…

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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: a) Supppose H is a 2 dimensional subspace of R³ with a basis {b₁,b2}, and y is a vector given by b₁…

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Q: Find a basis for the subspace of R° spanned by the following vectors. 6. 18 -3 -3 6 6. -18 -18 14…

A: We solve this by row reduced echolon  form

Q: If W is a subspace of ℝ4 whose dimension is 2 then is any set of 2 vector is a basis for W

A: Answer

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

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

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Q: The set B basis: [x]B = = - 3 -3 Find the coordinates of the vector x = -6 5 is a basis for R². [15]…

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