How do I calculate the solution of a linear system of equations, for example

x+2y-3z=	1
3x-2y+z=	1
x+y+z=	3

First create the matrix of coefficients

1. Enter [Matrx] "Edit"
2. Select the matrix "1:[A]", or another matrix.
3. Enter the dimension of the matrix, in this case 3x3
4. Enter in the coefficients:
   1. 1 [Enter]
   2. 2 [Enter]
   3. (-)3 [Enter]
   4. 3 [Enter]
   5. (-)2 [Enter]
   6. 1 [Enter]
   7. 1 [Enter]
   8. 1 [Enter]
   9. 1 [Enter]
5. Create the right-hand side matrix (vector) "b"
6. [Matrx] "Edit"
7. Select matrix "2:" [B]
8. Enter in the dimensions, in this case 3x1
9. Enter in the coefficients:
   1. 1 [Enter]
   2. 1 [Enter]
   3. 3 [Enter]
10. Get back to home screen [2nd] [Quit]
11. Find solution by [A]^-1[B]
    1. [Matrx] "Names" "[A]"
    2. [x^-1]
    3. [Matrx] "Names" "[B]"
    4. [Enter]

Note: If the matrix does not have an invers, the preferred method is to reduce it to row-reduced echelon form ("rref")

1. Enter in Augmented Matrix
2. [Matrx] "Edit" "[C]"
3. Enter in dimensions, 4x3
   1. 1 [Enter]
   2. 2 [Enter]
   3. (-)3 [Enter]
   4. 1 [Enter]
   5. 3 [Enter]
   6. (-)2 [Enter]
   7. 1 [Enter]
   8. 1 [Enter]
   9. 1 [Enter]
   10. 1 [Enter]
   11. 1 [Enter]
   12. 3 [Enter]
4. Get back to home screen [2nd] [Quit]
5. Find rref form of augmented matrix, by [Matrx] "Math" "rref" [Matrix] "Names" "[C]"