1. Define the vectors and as below, ²-[3] *-3 (a) Show that the vectors form a linearly independent set. (b) Define a third vector i 一周 Do the vectors , 7 and w form a linearly independent set? Show an argument to prove linear independence, or if linearly dependent provide scalars that illustrate a dependence relation. (c) Does span {u, v, w} = span { v, w}?

Q: Suppose V₁ = vector 1= Write five different vectors in Span{V₁, V2}. For each vector, show the…

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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: Q12: Let vector v = (1, 3) and vector w=(-4,-2). Write vector v as the sum of two orthogonal…

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Q: Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and…

A: Let S={u,v} be a linear independent set and generate W . Then W=span{u,v} .

Q: Q11: Let vector v = (-7, 5) and vector w=(2, 2). Write vector v as the sum of two orthogonal…

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Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

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

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Q: Consider a set of vectors S = {V₁, V2, V3} following statements is true? = {··]} Which one of the

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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 + 5v₂),…

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