The matrix is the reduced echelon matrix for a system with variables x1, x2, x3, and x4. Find the solution set of the system. (If the system has infinitely many solutions, express your answer in terms of k, where x1 = x1(k), x2 = x2(k), x3 = x3(k), and x4 = k. If the system is inconsistent, enter INCONSISTENT.)

1 0 0 0 | −1
0 1 0 0 | 2
0 0 1 0 | −4
0 0 0 1 | 0

(x1, x2, x3, x4) =

, , ,

x1 = -1, x2 = 2, x3 = -4, x4 = 0

If it wants everything in terms of what x4 equals then the system is inconsistent since x4=0

Step-by-step explanation:

Once you have it in that reduced row echelon form it's super easy.  

The first column is x1, second is x2 and so on.

The first row says x1 + 0x2 + 0x3 + 0x4 = -1, or in other words x1 = -1.  You can do this for all the rows.

this does mean that x4 = 0, so if the instructions are saying it wants everything n terms of x4, you can't do that so it is inconsistent.

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step-by-step explanation: