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

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.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Science:Math Exam Resources/Courses/MATH221/April 2009/Question 01/Hint 1 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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
