Science:Math Exam Resources/Courses/MATH152/April 2017/Question A 07
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Question A 07 

let be a system of linear equations, and let be the associated homogeneous system of linear equations. If is a solution to , and the solutions to are , give all solutions to . 
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 

Any solution to the system will be a sum of a particular solution to and a solution to the system . 
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. Any solution to the system is of the form 