Linear algebra

Linear equations

Fields

\begin{array}{rcr} D_{11} \, x_1 + D_{12} \, x_2 \, + \, ... \, + \, D_{1n} \, x_n &= z_1 \\ D_{21} \, x_1 + D_{22} \, x_2 \, + \, ... \, + \, D_{2n} \, x_n &= z_2 \\ &\vdots \\ D_{p1} \, x_1 + D_{p2} \, x_2 \, + \, ... \, + \, D_{pn} \, x_n &= z_p \end{array} This is a system of p linear equations in n unknowns.

Systems of linear equations

Matrices and elementary row operations

Row-reduced echelon matrices

Matrix multiplication

Invertible matricles