Science:Math Exam Resources/Courses/MATH221/April 2009/Question 01/Solution 1

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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