Explore BrainMass
Share

Explore BrainMass

    Difference between mapping R3 to R2 and the reverse

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

    Please help. I always have a hard time with Linear Algebra. What's the difference between mapping from R3 into R2 and mapping from R2 into R3?

    Why is the following not a linear transformation from R3 into R2?
    L(x) = (1 + x1, x2)^T

    And why is this one not a linear transformation from R2 into R3?
    L(x) = (x1, x2, 1)^T

    Thanks!

    © BrainMass Inc. brainmass.com October 9, 2019, 3:23 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/linear-transformations-example-problems-3055

    Solution Preview

    The difference between R3->R2 and R2->R3 is that they have different domain and range.
    For the mapping ...

    Solution Summary

    This shows why given mappings are or are not linear transformations.

    $2.19