Hi(adsbygoogle = window.adsbygoogle || []).push({});

Given a Vector Space V which has the basis [tex]\{ v_{1}, v_{2}, v_{3} \} [/tex] then I need to prove that the following set v = [tex]\{ v_{1}, v_{1}+ v_{2}, v_{1} + v_{2} + v_{3} \}[/tex] is also a basis for V.

I know that in order for v to be a basis for V then [tex]V = span \{v_{1}, v_{1}+ v_{2}, v_{1} + v_{2} + v_{3} \}[/tex], and the vectors of v need to be linear independent.

but by showing that the vectors of v are linear independent is the best way of show that v is a basis for V?

Sincerely

Fred

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Basis for a Vector space

**Physics Forums | Science Articles, Homework Help, Discussion**