= Augmented matrix
{title2=$[A\mid b]$}
The augmented <matrix> of a <linear system> $Ax=b$ appends the right-hand side as one extra column. Elementary row operations preserve its solution set. The <linear system> is consistent exactly when the coefficient <matrix rank> equals the augmented <matrix rank>, because this is equivalent to $b$ lying in the span of the columns of $A$. A larger augmented <matrix rank> produces a zero coefficient row with a nonzero right-hand side during <Gaussian elimination>.
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