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

Question

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

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

Try reading it slowly.

anonymous · Answer

ouch.