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: give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a.…

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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: 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: 7. Which of the following are linear combinations of = (0, -2, 2) and v = (1, 3, –1)? (a) (2, 2, 2)…

A: For a,

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

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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: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

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Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

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: 2. Find the projection from R³ onto its subspace spanned by (1, 2, −1)ª and (1,1,2).

A: Given that We  have  to  find  the projection from   onto  its  subspace spanned  by  .Let   be…

Q: Let u = (-7, 1, 5) and 7 = (5, 3, 4). —

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Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=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: Given that V1 = 5 3 V2 = 2 } V3 = 3 7 " 11 10 For what value(s) of h will y be in the subspace of H…

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Q: Determine a basis for the subspace of R that consists of vectors the form (a, b, c, a - 5b + 4c).…

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Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

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Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

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: 1

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Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

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Q: Q3. Point a base of this subspace of R*: W = { (x,y,z,t) ||-y+z=0,t - = 0 }

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