SOLUTION: Last one: Let T:R^n --> R^m be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in R^n. Prove that the set {T(v1), T(v2), T(v3)} is linearly dependent.

Algebra ->  College  -> Linear Algebra -> SOLUTION: Last one: Let T:R^n --> R^m be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in R^n. Prove that the set {T(v1), T(v2), T(v3)} is linearly dependent.       Log On


   

Question 40520This question is from textbook
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Let T:R^n --> R^m be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in R^n. Prove that the set {T(v1), T(v2), T(v3)} is linearly dependent.
I have proved it closed under addition and scalar multiplication, but am not sure if this is correct? Should I be looking at the trivial solution?
Thank you! This question is from textbook

Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
The set {v1, v2, v3} is linearly dependent so we could write

Now, because T is a linear transformation

So the set {T(v1), T(v2), T(v3)} is linearly dependent.