We are given a set of vectors S = {V1, V2, V3} in R 3 where...

We are given a set of vectors S = {V1, V2, V3} in R 3 where eV1 = [ 2 −1 3 ] , eV2 = [ 5 7 −1 ] , eV3 = [ −4 2 9 ]

Problem 1

• Prove that S is a basis for R^3 .

• Using the above coordinate vectors, find the base transition matrix eTS from the basis S to the standard basis e.

Problem 2 Using your answers in Problem 1

• Compute the base transition matrix STe from the standard basis e to the basis S.

• If eV = [ 5 1 7 ], compute SV (the coordinate vector of V with respect to the basis S). Use this to express V as a linear combination of the vectors in S.

Expert Solution

Colby Messinger answered 5 months ago

if {v1,v2,v3} is a linearly independent set of vectors, then {v1,v2,v3,v4} is too.

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