(a) On the set of people, (a, b) ∈R iff a and b both catch public transport  (b) On the set of 2D vectors, (u, v) ∈R iff u *  v = 0

Q: Let S be the subset of R2 consisting of all vectors of the form (a, b + 3). a) Show that (5, 2),…

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Q: Given two non-zero vectors a and b such that abs(a+b)=abs(a-b), find the value of a*b (dot product…

A: Given Two non-zero vectors a and b such that  a+b=a-b            ...........1 The dot product of and…

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: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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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: 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: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

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Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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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: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

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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: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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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: Let v1, V2, V3 and u be vectors in R". If u is orthogonal to each of v1, V2, and v3 then u is…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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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) = (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, + 5v2),…

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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: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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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: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Q: 7) Find all vectors v in F such that 2v + ) -)

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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,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…