Hi

Can someone kindly help me out with this and check
I am trying to solve the system of equations below in matrix form.

A matrix is follows:

\begin{pmatrix}3 &6  &-1  &-5  &4  &12 \\2& 4  &1  &0  &2  &5 \\1 &2  &-1  &-3  &1   &4 \\4& 8 & 0 &-4 & 2 & 8\end{pmatrix}


After making reduced row echelon form operations on it I have:

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



I have found that X1, X3 and X5 are lead variables and that X2 and X4 are free variables:
If I let X2 = s and X4 =t. Then:
X5= -2
X1= 2-2s+t
X3= -1-2s


Is this correct and is this how the answer should be presented?

Also, how can I find the basis for the U of \mathbb{R}4 from the matrix above?

Is this dimension of the U 3? and what is the dimension of U \perp?

I would appreciate any help