Matrix Algebra

Examples

EXAMPLE 1. Apply row operations to reduce the following matrix to an echelon form.

$\displaystyle \left[\begin{array}{rrrrr} 0 & -3 & -6 & 4 & 9 \\ -1 & -2 & -1 & 3 & 1 \\ -2 & -3 & 0 & 3 & -1 \\ 1 & 4 & 5 & -9 & -7 \end{array}\right]$

EXAMPLE 2. Apply row operations to transform the following matrix first into an echelon form, and then reduce it into the reduced echelon form.

$\displaystyle \left[\begin{array}{rrrrrr} 0 & 3 & -6 & 6 & 4 & -5 \\ 3 & -7 & 8 & -5 & 8 & 9 \\ 3 & -9 & 12 & -9 & 6 & 15 \end{array}\right]$

Matlab/Octave. Matlab/Octave comes with a rref function for row reducing matrices. Provided an augmented matrix A, type

> rref(A)

which produces a REF. The function

> rank(A)

can be called to compute the rank of matrix A.