In the definition of "soution vector" you say "**the** vector **x**". It should be "**a** vector **x** such that *x_1*, *x_2*, etc. satisfy the system of equations". See [linearSystems/reducedRowEchelonForm/matrices.tex](https://github.com/mooculus/linearAlgebra/blob/3523ba901527f80b2bb1eed0b1c711a4ad9992d6/linearSystems/reducedRowEchelonForm/matrices.tex)
In the definition of "soution vector" you say "the vector x".
It should be "a vector x such that x_1, x_2, etc. satisfy the system of equations".
See linearSystems/reducedRowEchelonForm/matrices.tex