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    Difference between mapping R3 to R2 and the reverse

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    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


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    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.