Question

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

Answer 1

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?

Answer 2

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

Answer 3

Try reading it slowly.

Answer 4

ouch.