Thread: linearly dependent

let T:R^n -> R^m be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in R^n. Explain why the set {T(v1),(v2),(v2)} is linearly dependent.

first, the latter set contains two elements which are equal..

assuming my corrections below...

Originally Posted by ssl000

let T:R^n -> R^m be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in R^n. Explain why the set {T(v1),T(v2),T(v3)} is linearly dependent.

if is linearly dependent, then WLOG, where and are scalars..

since is a linear transformation.
Thus you were able to express, WLOG, as a linear combination of and . Hence