You only need to find the inverse of the coefficient matrix
But does the inverse for this matrix exist?
Am I doing this correctly for matices?
x has subscripts 1 and 2
-2x + 2x = 2
3x - 3x = -3
|-2, 2, 2 |
|3, -3, -3|
-2(-1\2) = 1 so
|1, -1, -1|
|3, -3, -3|
-3(1) + 3 = 0 so
|1, -1, -1|
|0, 0, 0 |
The unique solution is x subcript 1 = ? and x subscript 2 = ?
Whenever you get a only series of zeros in the final step of Gaussian Elimination, it implies which is obvious and holds for any values of . In such case you do not get any unique solution, what you get is a family of solutions. In your problem, the family of solution is given by
So now, exactly what was the question? What you have shown so far is that both equations, and reduce to or . If the question was "is there a unique solution", the answer is "no". If the problem was to find all possible solutions, then , is a solution for any number, t, and all solutions are of that form.