12. Let W be the subspace of R4 spanned by the vectors, u₁ = (1, 2, 5, 3), u₂ = ալ (2, 3, 1, −4), u3 = (2,8, -3, -5) - Find a basis and dimension of W. Extend your basis of W to a basis of R4 (4.30)

Q: Find the matrix A' for T relative to the basis B'. T: R³ A' = R³, T(x, y, z) = (y + z, x - z, x -…

A: We have to Find the matrix A' for T relative to the basis B'.With the help of transformation and…

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

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Q: 5. Let ū = (0,2, 1), ở = (-1,0, 2) and w = (2,3,0). Find the coordinates of (2,2,2) with respect to…

A: This question is related to vector space. Solve in 2nd step .

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: 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: (iii) {(x, y, z) = R³: (x, y, z). (1, 1, 1) = 0} = {(x, y, z) = R³ : x+y+z = 0} = {(1,-1,0), (1, 0,…

A: Given,   {(x,y,z) ∈ R3:(x,y,z)-(1,1,1)=0}={(x,y,z) ∈ R³:x+y+z=0}=L(1,-1,0),(1,0,-1)} and we need to…

Q: Let R⁴ have a product in Euclidean. Use the Gram Schmidt process to convert the basis (u1, u2, u3,…

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Q: The second column of the matrix of change basis from the basis B={u=(1,1,1), v=(1,0,1) to the basis…

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Q: Consider the system of vectors (1,2, 1, 1)", (0,1,3, 1)", (0,3,2,0)", (0,1,0,0)". a) Prove that it…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

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Q: 4. (a) Let L be the line in R' spanned by the vector (1,1, 1, 1). Find a basis for the orthogonal…

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Q: → Suppose TR³ R³ be a linear bronsformation whose standard matrix has the basis (o 1, 2), (2, 1…

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Q: The second column of the matrix of change basis from the basis B={u= (1, 1, 1); v = (1,0,1); w=…

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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…

Q: 6. 34 The vectors v, = -9 and v2 = 5 form an orthogonal basis for W. Find an orthonormal basis for…

A: The solution is given as

Q: The second column of the matrix of change basis from the basis B = {u= (1,1,1); v = (1,0,1); w=…

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Q: B=[(1, 2, 1)", (0, 1, -1)', (1, 1, 1)"] is an ordered basis for , C =[(1, 1)', (2, 3) '] is an…

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Q: The second column of the matrix of change basis from the basis B = {u= (1,1,1); v = (1,0,1); w=…

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Q: 5. Consider the 4 x 5 matrix A = [u₁|u2|u3|u4| u5], where the columns are U₁= 2 , U2 = 5 Uz = -1 -2…

A: The  4×5  matrix  A= u1 | u2 | u3 | u4 | u5   where  u1=1234 , u2=5102 , u3=   2-1-2   3 , u4=  1…

Q: The second column of the matrix of change of basis from the basis B=(u=(1,1,1);v=(1,0,1);w=(0,1,1) )…

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Q: 1. Show that the vectors (1, 1,0), (1, 1, 1) and (1,0, 0) are a basis of R3. Find the coefficients…

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Q: How do I find a basis for {(2c, c, b)} | b, c ∈ R}? I tried writing it as a linear combination and I…

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Q: 3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, -1, 1) and (0, 0, -1, –1) form an orthogonal…

A: The solution is given as

Q: Find a basis for the subspace 96 4a + 6b W = E R2x2 a, b eR} of R2x2- 86 5a Ex: 1 4 6. A basis for W…

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Q: The second column of the matrix of change of basis from the basis B={u=(1,1,1); v= (1,0,1);…

A: What is Change of Basis: Any element of a vector space of finite dimension n can be uniquely…

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: 6. -4 Új = -5 U2 = 3 form a basis for R’ if and only if k #

A: Three vectors form the basis of ℝ3 if and only if the determinant of the matrix formed by the…

Q: 22. Find a basis for R4 that contains the vectors (3, 2, 3, 3) and (5, 4, 5, 5)

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Q: Question 4: [2 Mark] Determine whether or not the given vectors in R" form a basis for R": a) v₁ =…

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Q: - Let B = {v1, V2, V3} be the ordered basis of R3 consisting of V1 = 1 V2 = - V3 = 1 Find the…

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Q: 50° S. 80° R 60° 100 7. 7.

A: The measure of the arc length is double than the angle formed by that arc to the circumference of…

Q: 2.) Determine whether S = is a basis for R³. If it is write u = (6,3,6) as a linear combination of…

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Q: If B= {(1,1,0), (0,1,1), (−1,0,2)} is a basis of R³, then the coordinate vector of v= (8, -5, 3) in…

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Q: The third column of the change of basis matrix from the basis B={ur= (1,1,1); v= (1,0,1); w= (0,1,1)…

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