11. Find a basis of the following subspace of R4. all vectors of the form (a, b, c, d) where a + b – c + d = 0. (а) {(1,0,0, —1), (0, 1,0, —1), (0, 0, 1, 1)} (b) {(1,0,0, – 1), (0, 1,0, – 1)} (c) {(1,0, 0, – 1), (0, 1, 0, – 1), (0,0, 1, –1), (0, 1, – 1,0)} (d) {(1,0,0, –1), (0, 1,0, –1), (0, 1, –1,0)} (e) {(1,0, –1,0), (0, 1, 0, –1), (0,0, 1, – 1)} W 6. 6.

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

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Q: 14a.Show that the vectors w₁ = (0,2,0), W₂ = (3,0,3), W3 = (-4,0,4) form an orthogonal basis for R³…

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Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

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Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

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Q: . Determine if the vectors (3,2,0) , (-3,0,1) , and (1,1,–9) span all of R’ . Do these vectors form…

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Q: Let B = (1, x + 7, (x − 1)², 6׳) be an ordered basis for P3. Find the coordinate vector of f(x) =…

A: Given,                be an ordered basis for  and             To find the coordinate vector of…

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A: Given Vectors X =(1,1,1,1) and Y = (1,1,0,1) Now determine the orthogonal basis for R4

Q: Show that the vectors a, (1, 0, 0), a2 = (1, 1,0), a, = (1, 1, 1) form a basis of C'(C).

A:

Q: (1,1,..., 1)T be the column vector consisting of all 1s. Prove 0. 3. Let a = that La

A: Given: Let a=(1,1,......1)T  Then objective is to prove  La=0

Q: Find the coordinate vector [x] of x relative to the given basis B= (b₁,b2, b3 1 b1 = 0 B 2 b2 = 1 6…

A: here we have to find the coordinate vector of x

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Q: 1a. Given vectors v₁ = (1, 0, 0) and v₂ : (1, 0, 0) and v₂ = (0, 1, 0) in R³, find a vector V3 such…

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Q: Let p₁ (t) = 7+t², P₂ (t)=t-2t², P3(t) = 2+t-4t². Complete parts (a) and (b) below. a. Use…

A: The polynomials p1t, p2t and p3t belongs to the vector space P2 because P2 contains all the…

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Q: 1. Determine if the following vectors are linearly dependent or independent. Find an exact (non-…

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Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 16.- Obtain a…

A: Given vectors are a=(1,3,-1), b=(-2,1,3), c=(3,2,1), and d=(1,-1,2).

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A: In this question we have to find the terminal point of Q.

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Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

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Q: 1. (a) Find the matrix P that multiplies every vector (x, y, z) E R³ to produce the vector (3x+2y+z,…

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A: To determine the given vectors form of basis for or not.

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Q: E Let p 8x + 4x + 3. Find the coordinate vector of p relative to the following basis for P2, Pi = 1,…

A: We have to find the coordinate vector of P.

Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

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