Given linear transformations S: Rn --> Rm and T: Rn --> Rm, show the following:(adsbygoogle = window.adsbygoogle || []).push({});

a) S+T is a linear transformation

b) cS is a linear transformation

I know that since both S and T are linear transformations on their own, they satisfy the properties for being a linear transformation, which is that for some transformation T, T(x+y)=T(x) + T(y), and T(cx)=cT(x). So I tried doing the same sort of procedure for the sum of the transformations, so that (S+T)(x)=S(x) + T(x) and S(cx)=cS(x). This just doesn't seem like a very intricate way of proving the sums of linear transformations is a linear transformation and that a scalar multiplied by a linear transformation is a linear transformation.

Any help is greatly appreciated!

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# Homework Help: Proof of sums of linear transformations

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