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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?

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    We should be able to find a better title, but I can't think of a clear one right now. Also, I'd like to think that we don't make fun of people trying to learn in this community. You shouldn't worry about that.2012-01-21
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    Okay, thanks for the heads up. Is it possible that someone could help me get on the right track so I can answer this question correctly.2012-01-21
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    I would give it a little more time. I would bet money that someone will answer this within two hours; I will write something later if no one else has, certainly.2012-01-21
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    If the system was not consistent for all values of $f$ and $g$, what would the row reduction end up looking like?2012-01-21
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    (It only took three minutes!)2012-01-21
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    By the way, if you think David's answer has led you to solve the problem, then you can click the check mark below to accept it. This is a nice formality.2012-01-21

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