Matrix Problem of form Ax=B The matrix $A$ is given by
$$\left(\begin{array}{ccc}
1 & 2 & 3 & 4\\
3 & 8 & 11 & 8\\
1 & 3 & 4 & \lambda\\
\lambda & 5 & 7 & 6\end{array} \right)$$
Given that $\lambda$=$2$, $B$=$\left(\begin{array}{ccc}
2 \\
4 \\
\mu \\
3 \end{array} \right)$ and $X$=$\left(\begin{array}{ccc}
x \\
y \\
z \\
t \end{array} \right)$
Find the value of $\mu$ for which the equations defined by $AX=B$ are consistent and solve the equations in this case. State the rank of A.
So I began by reducing matrix $A$ to reduced row echelon form (kind of like taking the null space, except I'm dealing with $Ax=B$ instead of $Ax=0$) but since I have 5 variables and only 4 equations, I'm not sure how to continue onward.

Gauss-Jordan elimination is one of standard methods for solving linear systems.
$
\left(\begin{array}{cccc|c}
  1 & 2 & 3 & 4 & 2 \\
  3 & 8 &11 & 8 & 4 \\
  1 & 3 & 4 & 2 & \mu \\
  2 & 5 & 7 & 6 & 3
\end{array}\right)\sim
\left(\begin{array}{cccc|c}
  1 & 2 & 3 & 4 & 2 \\
  2 & 5 & 7 & 6 & 3 \\
  3 & 8 &11 & 8 & 4 \\    
  1 & 3 & 4 & 2 & \mu
\end{array}\right)\sim
\left(\begin{array}{cccc|c}
  1 & 2 & 3 & 4 & 2 \\
  0 & 1 & 1 &-2 &-1 \\
  0 & 2 & 2 &-4 & 0 \\
  1 & 3 & 4 & 2 & \mu
\end{array}\right)\sim
\left(\begin{array}{cccc|c}
  1 & 0 & 1 & 8 & 4 \\
  0 & 1 & 1 &-2 &-1 \\
  0 & 0 & 0 & 0 & 0 \\
  1 & 3 & 4 & 2 & \mu
\end{array}\right)\sim
\left(\begin{array}{cccc|c}
  1 & 0 & 1 & 8 & 4 \\
  0 & 1 & 1 &-2 &-1 \\
  0 & 3 & 3 &-6 & \mu-4 \\
  0 & 0 & 0 & 0 & 0
\end{array}\right)\sim
\left(\begin{array}{cccc|c}
  1 & 0 & 1 & 8 & 4 \\
  0 & 1 & 1 &-2 &-1 \\
  0 & 0 & 0 & 0 & \mu-1 \\
  0 & 0 & 0 & 0 & 0
\end{array}\right)
$
In this case you should discuss what happens depending on the value of $\mu$. The third row corresponds to the equation $0x+0y+0z+0t=\mu-1$, or - to put it simpler - $0=\mu-1$. What can you say about solutions of this system if $\mu-1=0$? What can you say if $\mu-1\ne0$?
You can also check your work in WA like this or this
