MATH221 April 2009
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Find all values of c such that the system of equations below is consistent. For these values of c write the general solution of the system in the parametric vector form.
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From the system we are able to get the following matrix. By doing Gaussian Elimination, we are able to get the matrix below
If we look at the 3rd row of this matrix, we have .
In the case of , the matrix becomes
This implies that and are free variables and the general solution is
On the other hand, if , we can easily see that .
Therefore, the matrix becomes
which can be solved easily. The general solution is