Find a basis for the subspace of ps W= , X3, X4, Xs )x1 + 2x, + x5 = 0} OA {(1.0,0,1). (0,-1,0,0,2). (0,0,1,0,0). (0,0,0,0,1)} O B. No correct answer OC. OD (1.000.1). (0-1,0,0.2) (0.0. 1.0.0)} OE (1.0,00.1).(0-1.0.0.2), (0.0.0.0.1)}

Q: The set W : 3x - y = z -5w = 0} is a subspace of R*. What is the dimension of W Select one: а. 1 b.…

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Q: S- ((2, 5, -3, -5), (-2, -3, 2, -2), (1, 3, -2, 5), (-1, -5, 3, 2)} 00

A: Given that S=2, 5,-3,-5, -2,-3, 2,-2, 1, 3,-2, 5, -1,-5, 3, 2. The objective is to find a basis for…

Q: Q8) Explain why S is not a basis a) S = {(2,1,–2), (–2, –1,2), (4,2, –4)} for R³ b) S = {2,2,x +…

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Q: Find a basis for the subspace of R* spanned by S. s 3D {(2, 5, -3, -2), (-2, -3, 2, -3), (1, 3, —2,…

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Q: Find a basis for the subspace of R3 spanned by s. S = {(1, 5, 9), (-1, 6, 9), (2, 6, 1)}

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Q: In each part, find a basis for the given subspace of R4 .(2) All vectors of the form (a, b, c, d)…

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Q: - (-, s) Find a basis for the subspace W C R', consisting of all the vectors orthogonal to the…

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W⊥

A: The orthogonal complement of the subspace W is the set W⊥=v∈V : v, w=0 for all w∈W and the…

Q: 142 Q2. Let A = Determine a basis for each of the subspaces CS(A"), |3| 316 N(A), CS(A), and N(A").

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Q: Let W be the subspace of R4 spanned by S V₂ = (1, 1, 1, −1), Let V₁ =(2, 1, 2, 1), W₁ = (1, 1, 0,…

A: (a) S={v1=(2,1,2,1) , v2=(1,1,1,−1) , v3=(5,3,5,1) , v4=(−1,−2,−1,4)}Subspace W spanned by S.A…

Q: Find a basis for the subspace of R'consists of all vectors of the form (a, 2a + b, b, 0). State its…

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Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

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Q: Given v = find the coordinates for v in the subspace W spanned by -7 u1 = and uz -1 -28 Note that uj…

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Q: -F -5 8 generated by v₁ and v2. 3. Let vi 2 3, V₂ = -5 and w = 8 B 2 Determine if w is in the…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(-11, 6, 4, 8), (-6, 3, 2, 4), (-2, 1, 1, 2),…

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Q: Asap show correct work and answer

A: ∴any vector in the null space can be written by using the vector (1,-1,1).So, dimension of the null…

Q: X1 ER* satisfying the X3 X2 6. Show that the set of all vectors XA equations 3x1 - 2x2- X3-4x4 = 0…

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Q: Find a basis for the subspace of R* spanned by S. S = {(64, -21, 9, 27), (-21, 7, -3, -9), (6, -2,…

A: B is called the basis for the subspace of ℝ4 spanned by S  if i) B is linearly independent  ii) B…

Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

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Q: Which of the following is a subspace of p2? O a. R2 x, e R W = Зх, + 1 1. Ob. W = ER| x*2 2 0 C. ER?…

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Q: 7. Find a basis for, as well as the dimension of the subspace of R* generated by the vectors (1, -1,…

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Q: Let V₁ = V₁ and v2. 1 -4 , V2' = -2 3 and w= -3 Determine if w is in the subspace of R³ generated by…

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Q: -8 -5 -1 6 -4 --- U₁ = -5 -6 -7 -10 1 -18 Compute the distance d from y to the subspace of R4…

A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

Q: Find the projection of the vector v onto the subspace S. -1 1 -1 S = span v = -1 |-2/3 -2/3 projs v…

A: To find the projection of the vector v onto the subspace S, where

Q: 1

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Q: Find a basis for the subspace of R W- (*,X,X3, X4, X )x + 2xz + Xg = 0) {(1.0.00.1).(.-1.0.0.2).…

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