Finding solutions of matrix and basis question

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:

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

I have found that X_{1, }X_{3} and X_{5} are lead variables and that X_{2 }and X_{4 }are free variables:

If I let X_{2 }= s and X_{4 }=t. Then:

X_{5}= -2

X_{1}= 2-2s+t

X_{3}= -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 ^{4} from the matrix above?

Is this dimension of the U 3? and what is the dimension of U^{
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}?

I would appreciate any help (Itwasntme)