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**[SOLVED] Linear transformations**

**1. Homework Statement**

Determine whether the following maps are linear transformations. (proofs or counterexamples required)

a.) L: R^2[tex]\rightarrow[/tex]R^2,

(x1)

(x2)

[tex]\mapsto[/tex]

(2x1 + 3x2)

(0)

The brackets should be two large brackets surrounding the two vectors.

**3. The Attempt at a Solution**

I've been reading about linear transformations and i know i have to show something like:

L(x1+x2)= L(x1) +L(x2) and L(cx1)= cL(x1) where c is a scalar.

Is this right and i should treat x1 and x2 separately rather than the vector including x1 and x2 as one element of R^2?

What im trying to say is, do i need to define a vector (y1, y2) aswell in the set of R^2?

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