# 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

Thanks!

Â© BrainMass Inc. brainmass.com May 24, 2023, 12:49 pm ad1c9bdddfhttps://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.

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