# Thread: matrix system of equations help

1. ## matrix system of equations help

Determine the solutions of the system of equations whose matrix is row equivalent to
$

\begin{bmatrix}1&0&-1&1\\ 0&1&3&1\\ 0&0&0&0\end{bmatrix}
$

2. Originally Posted by wonderstrike
Determine the solutions of the system of equations whose matrix is row equivalent to
$

\begin{bmatrix}1&0&-1&1\\ 0&1&3&1\\ 0&0&0&0\end{bmatrix}
$

Since the matrix is already in Reduced Row eschelon form and it has two leading ones, this tells us that there will be one parameter in our solution

Since we have one parameter let

$z= t$

the 2nd row tells us we have

$y+3z=1 \iff y=1-3z \iff y=1-3t$

and the first row tells us

$x-z=1 \iff x=z+1 \iff x=t+1$

Now our solution is the vectors are

$\begin{bmatrix}
x \\
y \\
z \\
\end{bmatrix}=
\begin{bmatrix}
t+1\\
1-3t \\
t \\
\end{bmatrix}=
\begin{bmatrix}
t\\
-3t\\
t \\
\end{bmatrix}+
\begin{bmatrix}
1 \\
1 \\
0\\
\end{bmatrix} =$

$
t\begin{bmatrix}
1\\
-3\\
1 \\
\end{bmatrix}+
\begin{bmatrix}
1 \\
1 \\
0\\
\end{bmatrix}$

So the constant vector is your particlular solution and and linear combination with the first will be a solution

3. is there another way to go about this? That def doesn't look familiar at all to me.

4. Originally Posted by wonderstrike
is there another way to go about this? That def doesn't look familiar at all to me.
Okay... what class is this for? What part doesnt make sense. Are you familiar with matrices? Please let me know, I and I will try to help.