What does this look like?

I'm given a matrix which has a variable in it, and the question asks to determine the value variable such that the augmented matrix of the linear system has infinitely many solutions.

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- Sep 16th 2007, 03:37 PMThomasMatrices with infinitely many solutions
What does this look like?

I'm given a matrix which has a variable in it, and the question asks to determine the value variable such that the augmented matrix of the linear system has infinitely many solutions. - Sep 16th 2007, 03:55 PMPlato
Gee, I think we need to see the exact question.

- Sep 16th 2007, 08:44 PMThomas
Determine the value of $\displaystyle h$ such that the matrix is the augmented matrix of a linear system with infinitely many solutions.

$\displaystyle

\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;7 & -7 & 3\;\\\;14 & h & 6\end{vmatrix}

$

That's the exact question. :) - Sep 16th 2007, 09:13 PMJhevon
- Sep 17th 2007, 04:25 AMThomas
That's what I'm asking... I'm not sure.

I do notice that the second equation is double the first (except for $\displaystyle h$.) - Sep 17th 2007, 05:02 AMPlato
- Sep 17th 2007, 06:58 AMJhevon
as Plato hinted, you're on the right track. remember, we have infinitely many solutions if we have some parameter replacing one of our variables. this means there can be no leading 1 in the column that corresponds to that variable. what is the link between that property and one line being a multiple of another?

- Sep 17th 2007, 05:28 PMThomas
Okay, so make the bottom row 0's?

Do I want the top row to be zero's as well? Or do I reduce the top row as normal? I'm thinking reduce as normal... - Sep 17th 2007, 05:35 PMJhevon
yes. what does h have to be to do that?

Quote:

Do I want the top row to be zero's as well? Or do I reduce the top row as normal? I'm thinking reduce as normal...

- Sep 17th 2007, 05:40 PMThomas
- Sep 17th 2007, 05:42 PMJhevon
- Sep 17th 2007, 05:52 PMThomas
Thank you for the help. :)