- #1
Mathman23
- 254
- 0
Hi
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
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
Last edited: