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Matrix algebra : Find the matrix C such that N(A) = R(C)

Member advised to present information more clearly in future posts
Problem Statement
So I am wondering what the correct x[SUB]4[/SUB] is. From the method I was taught to expressing vector form I think that x[SUB]4[/SUB] should be the vector :
-3
0
4
1

But all of the examples I have come across translate into vector form directly after the RREF which would make it :
-3
4
0
1

Could someone clarify this for me?
Relevant Equations
Matrix A is the first matrix shown in my attached image
N(A) is the nullspace of A
R(C) is the range of C
20190325_204949.jpg
 
32,348
4,133
So what is the actual problem statement? Your relevant equations are merely a partial statement of the problem, but nowhere is it shown what A and C are. Presumbly N(A) means the nullspace of A. Is R(C) the rowspace of C?
 
So what is the actual problem statement? Your relevant equations are merely a partial statement of the problem, but nowhere is it shown what A and C are. Presumbly N(A) means the nullspace of A. Is R(C) the rowspace of C?
Well my question pertains to X4 which is the 4th column. I wrote down what the Matrix A is in A=[]
I have to find C which will be X2 and X4 combined into a matrix.

N(A) is the nullspace of A
R(C) is the rowspace of C

Sorry I should have mentioned that from the start I hope this is enough clarification.
 

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