Explore BrainMass
Share

Explore BrainMass

    Linear Combinations, Basis and Transformations

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com October 9, 2019, 6:25 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/linear-combinations-basis-transformations-87843

    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.

    $2.19