Solve the system `{:(x-y+2z=-3),(2x+y-z=0),(-x+2y-3z=7):}`

Answer

`x=-2, y=7, z=3`

Explanation

The matrix form of this system is AX = B, where `A={:[(1,-1,2),(2,1,-1),(-1,2,-3)]:},X={:[(x),(y),(z)]:},andB={:[(-3),(0),(7)]:}.A` is the coefficient matrix, and B is the constant matrix.
This system can be represented by the single `3xx4` matrix `{:[(1,-1,2,-3),(2,1,-1,0),(-1,2,-3,7)]:}`. In general, if
there were n equations and n variables, then matrix A would have n rows and n+1 columns
You can use the calculator to transform this matrix t reduced row echelon from. This trans- formation involves multiplying a row a constant, or multiplying a row by a constant and adding the result to another row, and replacing the second row with the sum. (This is the same procedure used to solve a system of two equations in two variables.) These operations are done with the intent of transforming the first three columns into a `3xx3` identity matrix. AS this is done the fourth column transforms into the solution. In the example above,
`{:[(1,-1,2,-3),(2,1,-1,0),(-1,2,-3,7)]:}to{:[(1,0,0,-2),(0,1,0,7),(0,0,1,3)]:}," so "x=-2,y=7,z=3`.