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.

Printable View

- December 20th 2008, 01:24 PMssl000linearly dependent
let T:R^n -> R^m be a linear transformation, and let {

**v**1,**v**2,**v**3} be a linearly dependent set in R^n. Explain why the set {T(**v**1),(**v**2),(**v**2)} is linearly dependent. - December 20th 2008, 06:37 PMkalagota
first, the latter set contains two elements which are equal..

assuming my corrections below...

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