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Linear Combinations, Basis and Transformations

1. Given a basis B = { u1 = [1, 2], u2 = [2, 1] } for R^2, express u = [7, -2] as a linear combination of u1 and u2. How many ways can you do this?
(in this problem...the u1 and u2 should actually be u sub 1 and u sub 2...I couldn't do that notation here....also the u1, u2, and u should all be bold to represent vectors)

2. Let T be the reflection through the x - axis in R^2. Is T a linear transformation? If so, find the standard matrix of T.

Solution Preview

1. Let u=x*u1+y*u2, then we have
[7,-2]=x*[1,2]+y*[2,1]=[x+2y,2x+y]
So we get a ...

Solution Summary

Linear Combinations, Basis and Transformations are investigated.

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