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