Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 04 (c)
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Question B 04 (c) 

The augmented matrix below for a linear system is put in reduced row echelon form with row operations. Write one of the following:
(c) 
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 

Recall that if the matrix has a row of zeros then the corresponding value in the augmented part of the matrix must be zero or there is no solution. 
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 matrix, we see that the last row is all zeros (including the augmented part) and so we have a free parameter. Since there are more columns than rows to this matrix (the matrix is rank deficient) then there is a second free parameter. Let the free parameters be x_3 and x_4. Then from the second row we have and from the first row we have Therefore we have two null vectors and as well as a particular solution so that the solution is There are an infinite number of solutions. 