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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

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