I am new to this so please don't make fun of me. The question:
Suppose that the linear system $$ \begin{align*} 2x + 4y &= f \\ cx + dy &= g \end{align*} $$ is consistent for all possible values of $f$ and $g$. What can you say about the coefficients $c$ and $d$? (Hint: What does row reduction tell you?)
I learned that this would be the augmented matrix: $$ \begin{bmatrix} 2 & 4 & f \\ c & d & g \end{bmatrix} $$ So with row reduction: Each row has to have a leading coefficient of $1$ and where the leading coefficient is $1$ then the the rest in the column has to be zeros if the leading coefficient is $1$.
Am I on the right track?