Science:Math Exam Resources/Courses/MATH152/April 2012/Question 02 (c)
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Question 02 (c) 

Consider the following system of linear equations where a,b, and c . Give that x=y=z=1 is a particular solution to the system above, determine the values of a, b, and c. Then find all the solutions in this case and express them in parametric 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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Multiply the matrix with the vector of x, y, z. 
Hint 2 

Once we have a particular solution, how can we write the general solution using our work from part (b)? 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. If we multiply the matrix A to the vector [1,1,1] we get and therefore a=3, b=2, and c=1. If we set those values permanently then we know that [1,1,1] is a particular solution to the problem. However, from part(b) we have that the solution to the homogeneous problem was and therefore we can write that the general solution is the sum of the particular and homogeneous solution, 