Exercise 1.8 Consider the subspace W = ((1,1,1,1), (1,1,0,0)) of R¹ and the vectors v₁ = (2,2,3,3), v₂ = (0, 1, 1,0), v3 = (1,-1,0, 1). a) Tell which among the vectors v; satisfy dim(W + (v₁)) = 2. b) Tell which among the vectors v; satisfy W (vj). c) Determine a basis and the dimension of (W+ (v₁)) (W+(v₂)). d) Determine a basis and the dimension of (W+ (v2)) + (W + (v3)).

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, V1 + V2,…

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Q: Use the function to find the image of v and the preimage of w. T(v1, v2, v3) = (4v2 - v1, 4v1 +…

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Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the…

A: We will find out the required solution.

Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: Use the function to find the image of v and the preimage of w. T(Vy. V2) = ( V2, 2v1 - v2), v = (7,…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 +…

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Q: Use the function to find the image of v and the preimage of w. T(V,, V2, V3) = (4v, - v,, 4v, +…

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Q: Q-2: a) combination of the vectors X = (1,2,3,0) and Y = (2,1,6,0). b) a linearly independent set of…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4V1 +…

A: Given  T(v1,v2,v3) = (4v2-v1,4v1+5v2)Image of v is given by T(1,-2,-4) = (-9,-6) hence (a). the…

Q: V2, V1 + v2, 2v1 - v2 ), v = (9, 9), w = (-3/2, 2, -8) (a) the image of v (b) the preimage of w (If…

A: This is a problem of vector calculus.

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, Vị + V2,…

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Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 +…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v, +…

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Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = V2, V1 + V2, 2v, - v2 2…

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Q: Show that VI = (1,0,1) , v, = (1,1,0) , v3 = (1,1,1) span R'. Express vector v= (2, 1, 3) as linear…

A: v1 ,v2 ,v3 ,...,vn span R^n if det(v1,v2,...,vn) is non zero