- #1
misterau
- 20
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Homework Statement
Let V be the vector space spanned by v1 = cos^2(x) , v2 = sin^2(x) , v3 = cos(2x) .
Show that
{v1 ,v2 ,v3} is not a basis for V , then find a basis for V .
Homework Equations
The Attempt at a Solution
(-1)*cos^2(x) + (1)*sin^2(x) + (1)*cos(2x)=0
{v1 ,v2 ,v3} is not linearly independent, so is not a basis for V.
I am not sure how to do the next part of the question, "find a basis for V" .
I am thinking its probably {v1,v2}. As v1 and v2 are linearly independent. However how do I show this set spans V?