Suppose p1, p2, p3, p4 are specific polynomials that span

Chapter , Problem 6E

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QUESTION:

Problem 6E

Suppose p1, p2, p3, p4 are specific polynomials that span a two-dimensional subspace H of . Describe how one can find a basis for H by examining the four polynomials and making almost no computations.

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QUESTION:

Problem 6E

Suppose p1, p2, p3, p4 are specific polynomials that span a two-dimensional subspace H of . Describe how one can find a basis for H by examining the four polynomials and making almost no computations.

ANSWER:

Solution 6E

Step 1 of 2

Consider a two-dimensional subspace H of  such that

 for some specific polynomials

The objective is to determine a basis for H without compute anything.

A set of two vectors is linearly dependent if any vector is a scalar multiple of the other, or any of the vectors in the set is a zero vector.

To form a basis for H, need to exclude the vectors, which are the linear combinations of others, or zeros one by one.

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