Here is the problem I have been asked to solve:(adsbygoogle = window.adsbygoogle || []).push({});

Assume that m < n and l1, l2, . . . , lm are linear functionals on an n-dimensional vector space X.

(a) Prove there exists a non-zero vector x in X such that the scalar product < x, lj >= 0 for 1 <= j <= m. What does this say about the solution of systems of linear equations?

(b) Under what conditions on the scalars b1, . . . , bm is it true that there exists a vector x in X such that the scalar product < x, lj >= bj for 1 <= j <= m? What does this say about the solution of systems of linear equations?

I am having trouble understanding the concept of a linear functional and how it relates to the vector space X.

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# Homework Help: Linear functionals

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