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

[Arturo Andujo]

Homework 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

 

[Mark44]

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?

 

[Arturo Andujo]

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.