## College Algebra (10th Edition)

$[A|B]=\left[\begin{array}{rrr|r} {1}&{-1}&{1}&{10}\\ {3}&{3}&{0}&{5}\\ {1}&{1}&{2}&{2}\end{array}\right]$
Standard form of a linear equation: $a_{i1}x_{1}+a_{i2}x_{2}+\cdots+a_{in}x_{n}=b_{i}$ ... the index i indicates that it is the i-th equation of a system of equations. Augmented matrix $[A|B]$ of a system written in standard form: - has as many rows as there are equations, - has one more column than there are variables, - has the constants of the RHS in the last column, $B=[b_{i}]$ - has the entries of the coefficient matrix $A=[a_{ij}]$ to the left of the last column. --- The system is in standard form $A=\left[\begin{array}{lll} 1 & -1 & 1\\ 3 & 3 & 0\\ 1 & 2 & 2 \end{array}\right],\quad B=\left[\begin{array}{l} 10\\ 5\\ 2 \end{array}\right]$ $[A|B]=\left[\begin{array}{rrr|r} {1}&{-1}&{1}&{10}\\ {3}&{3}&{0}&{5}\\ {1}&{1}&{2}&{2}\end{array}\right]$