Matrices

Consider the system of equations below

\[\begin{align*} & 2x &&+ y &&- z &&= 1 \\ & 3x &&+ 4y &&+ 2z &&= 13 \\ & x &&- 5y &&- 2z &&= 0 \end{align*}\]

Coefficient Matrix

The coefficient matrix is a matrix of just the coefficients in the system of equations. Applied for the system above,

\[\begin{bmatrix} 2 & 1 & -1 \\ 3 & 4 & 2 \\ 1 & -5 & -2 \end{bmatrix}\]

Augmented Matrix

The augmented matrix is like the coefficient matrix but with the sums.

\[\begin{bmatrix} \begin{array}{ccc|c} 2 & 1 & -1 & 1 \\ 3 & 4 & 2 & 13 \\ 1 & -5 & -2 & 0 \end{array} \end{bmatrix}\]