# Solutions to these matrices

• May 22nd 2012, 05:46 AM
zzizi
Solutions to these matrices
Hi

This may be basic, but i'd really appreciate some help.
The 3 augmented matrices are in reduced row echelon form. For each state *with a reason* the number of solutions

$\begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}$

$\begin{pmatrix}1 & 2 & 0 &1 \\0 & 0 & 1 &2 \\0& 0 & 0&0\end{pmatrix}$

$\begin{pmatrix}1 & 0 & 0 &1 \\0 & 1& 0 &2 \\0& 0 & 1& 3\end{pmatrix}$
• May 22nd 2012, 07:29 AM
Prove It
Re: Solutions to these matrices
Quote:

Originally Posted by zzizi
Hi

This may be basic, but i'd really appreciate some help.
The 3 augmented matrices are in reduced row echelon form. For each state *with a reason* the number of solutions

$\begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}$

$\begin{pmatrix}1 & 2 & 0 &1 \\0 & 0 & 1 &2 \\0& 0 & 0&0\end{pmatrix}$

$\begin{pmatrix}1 & 0 & 0 &1 \\0 & 1& 0 &2 \\0& 0 & 1& 3\end{pmatrix}$

Try writing each row as an equation with the variables. The answers should then be obvious...
• May 22nd 2012, 08:57 AM
zzizi
Re: Solutions to these matrices
The soln to this matrix is x1 = 1-2x2
X3=0
But is that enough as explanation?
$\begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}$
• May 22nd 2012, 06:55 PM
Prove It
Re: Solutions to these matrices
Quote:

Originally Posted by zzizi
The soln to this matrix is x1 = 1-2x2
X3=0
But is that enough as explanation?
$\begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}$

Since x_2 is a free variable, wouldn't that mean there are an infinite number of solutions?