Linear Algebra: how to find basis for H "by examination"

[Siesta]

Suppose p1 , p2 , p3 , p4 are polynomials so that Span {p1 , p2 , p3 , p4 } = H is a two-dimensional subspace in P. Describe how to ?nd a basis for H by examining the four polynomials and doing almost no work.

Could I have a hint?

 

[galactus]

Re: Linear Algebra help needed

It already says it spans. Now, if they are linearly independent, you're in business.

 

[Siesta]

What does it mean for the subspace to be two-dimensional?

 

[daon]

What does it mean for the subspace to be two-dimensional?

It will be spanned by two independent vectors.

 

[Siesta]

So for the question above, if you take two polynomials out of p1, p2, p3, p4, for example p1 and p3, and they're linearly independent, then it's a basis for H?

 

[daon]

So for the question above, if you take two polynomials out of p1, p2, p3, p4, for example p1 and p3, and they're linearly independent, then it's a basis for H?

You got it .