Science:Math Exam Resources/Courses/MATH152/April 2016/Question B 02 (c)
Question B 02 (c) 

In the system below, , , and are variables, and and are constants.
(c) For what value or values of and (if any) does the system have no solutions? 
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Hint 

A system of linear equations has no solution if a row echelon form of the augmented matrix has a row consisting of all zeros on the left hand side together with a nonzero entry on the right hand side. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By (b), a row echelon form of the augmented matrix is
The system of linear equations has no solution if a row echelon form of the augmented matrix has a row with all zeros on the left side together with a nonzero entry on the right hand side. The first two rows of this augmented matrix are not zero rows. However, if , then the third row would consist of all zeros on the left side. In order to make the right hand side nonzero, we would need i.e., or Therefore, the answer is . 