I'm not even sure if this problem is technically solvable, but we're given 4 simultaneous equations with 4 variables. We have to put these equations in matrix form (did that, used the coefficients), determine the determinant, construct the adjoint and inverse matrices, and then finally solve for the unknowns with the help of the inverse. I found the determinant to be 0 (used a program online and my graphing calc.), I found the adjoint (online program), and tried to find the inverse (calculator and program), for which there was no inverse. I know there is no inverse if the determinant is zero (the matrix is singular), but does this mean that there is no way to solve for the unknowns? I'm just not sure if there's one little thing I'm missing (and yes I checked the initial matrix like 5 times, I even solved this way with the calculator and program using the example problem from class), or if I'm just supposed to explain to the teacher that half of this homework problem can't technically be solved (he really doesn't give us homework problems like this) and explain why. Here's the equations also:
X1 + (2)X2 + X3 + X4 = 2
(2)X1 - X2 + (3)X3 + X4 = 10
(3)X1 + X2 + X3 - X4 = -3
X1 + (2)X2 - X3 - X4 = 5
So my initital matrix should be
1-2-1-1
2-(-1)-3-1
3-1-1-(-1)
1-2-(-1)-(-1)
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