Row equivalence

The two systems of linear equations

$\displaystyle \left\{\begin{array}{rrrr}
x_1 & -2 x_2 & + x_3 = & 0 \\
& 2 x_2 & -8 x_3 = & 8 \\
-4 x_1 & +5 x_2 & +9 x_3 = & -9
\end{array}\right.$    and $\displaystyle \quad
\left\{\begin{array}{rrrr}
x_1 & -2 x_2 & + x_3 = & 0 \\
& 2 x_2 & -8 x_3 = & 8 \\
& -3 x_2 & +13 x_3 = & -9
\end{array}\right.
$

are equivalent in the sense that they should have the same solution. Equivalently by applying row operations we obtain the matrices

$\displaystyle \left[\begin{array}{rrrr}
1 & -2 & 1 & 0 \\
0 & 2 & -8 & 8 \\
-...
...rrr}
1 & -2 & 1 & 0 \\
0 & 2 & -8 & 8 \\
0 & -3 & 13 & -9
\end{array}\right]
$

The symbol ``$ \sim$'' indicates that the two matrices are row equivalent.



Department of Mathematics
Last modified: 2005-10-21