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: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

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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: 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: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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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: V₁ = V1 V3 = V2= 4 [ 3 [-1] 2 3]

A: We use the properties of linear combination to

Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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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: (2) Let vị = ( 2 = (2),v3 1 of the vector space R³. (2a) Does the vector v = (6 belong to…

A: Linearly independent vectors: The set of vectors v1, v2, ..., vn is said to be linearly independent…

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

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Q: The vector -3 (GIE) -1 -4 0 -7 vectors -3 2 belongs to the span of the 5 Select one: O True O False

A: Given: W=span-3-10, -1-4-7. To check v=-325∈W.

Q: Determine whether the vectors ?→ = (2,−1,3), ? → = (1,1,−2), and ? → = (3,−1,5) span ℝ?. If not find…

A: Span: Let us consider the set of  vectors S={v1,v2,v3,......vn} in a vector space V is said to be…

Q: Are the vectors ū = [4 -5 4], v = [2 2 -3] and w = [-1 -5 2] linearly independent? Choose If they…

A: To find Whether the given vectors are limearly independent or not.

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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Q: 3) Check whether the vectors V, =[1 3 3 5.V =[3 10 6 7]'.v, = [2 7 3 2] e linearly are independent.

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