Question

How do I write the matrix `((4,3,7),(1,1,5),(4,5,7))` in reduced row echelon form?

Answer 1

If your question is correct, then your system is inconsistent because it reduces to the identity matrix and you get `0=1` in the third row.

Again, if your question is correct, you have an overdetermined system of linear equations, that is:

`4x+3y=7`
`x+y=5`
`4x+5y=7`

For a regular system of linear equation, you would have an `n` by `n+1` matrix, that is `n` rows and `n+1` columns. We fill the first 3 columns with the coefficients for the variables and we fill the last column with the constants of the equations.

My guess is that your question is incorrect and you are missing the constants from your matrix.