How would i go about using properties of row reduction to explain why the equation $Ax - b = 0$ is true?
I am not sure how to attack this. I know that $Ax=b$ where $b$ is a linear combination of the matrix $A$ so it would make sense that if we subtracted our summed vector $b$ from the combination of each vector then we would have $0$. Beyond that i am not sure how to further explain using "properties of row reduction". Can anyone help?
edit: anyone?