A matrix-vector product (Definition MVP) is a linear combination of the columns of the matrix and this allows us to connect matrix multiplication with systems of equations via Theorem SLSLC. Row operations are linear combinations of the rows of a matrix, and of course, reduced row-echelon form (Definition RREF) is also intimately related to solving systems of equations. In this section we will formalize these ideas with two key definitions of sets of vectors derived from a matrix.

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- September 11th, 2017
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##### The matrix equation Ax=b has a solution if and only if b is a linear combination of the columns of A. math.la.t.mat.eqn.lincomb