Skip to main content Contents Prev Up Next \(\newcommand{\avec}{{\mathbf a}}
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\)
Chapter 7 Linear independence
In the previous section, questions about the existence of solutions of a linear system led to the concept of the span of a set of vectors. In particular, the span of a set of vectors \(\vvec_1,\vvec_2,\ldots,\vvec_n\) is the set of vectors \(\bvec\) for which a solution to the linear system \(\left[\begin{array}{rrrr}
\vvec_1\amp\vvec_2\amp\ldots\amp\vvec_n \end{array}\right] ~\xvec
= \bvec \) exists.
In this section, we turn to the uniqueness of solutions of a linear system, the second of our two fundamental questions. Uniqueness: If there is a solution to the equation \(A\xvec=\bvec\text{,}\) is it unique? This will lead us to the concept of linear independence.
