## anonymous 4 years ago LINEAR ALGEBRA : Prove that the transformation LA:R^n R^m induced by the m x n matrix A is linear.

1. anonymous

Linear transformations produced by matrices are defined as functions as follows. (here, taking your problem's example of transformation $$LA$$).$LA(\vec x) = A\vec x$Here, $$\vec x \in \mathbb R^n$$ and $$A\vec x \in \mathbb R^m$$, as you specified. Remember, if you want to show that $$f:A\rightarrow B$$ is a linear transformation, you need to show that for all $$a_1, a_2 \in A$$ and all constants $$C_1, C_2 \in \mathbb R$$ that $f(C_1a_1+C_2a_2)=C_1 f(a_1) + C_2 f(a_2).$Does this give you enough information to proceed?

2. anonymous

wow, i dont really understand i tho. can u say it more in english than math lol

3. anonymous