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Sara L.

asked • 06/15/19

Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions

Hi, i reduced this however i am stuck when it comes to finding the 3 solutions, (infinity, one , no solutions). I am confused with what do they mean with them! would appreciate it if someone can answer what do they mean in general and in this question!

The matrix after reduction:

1 1 0 2

0 1 1 2

0 0 2 2

0 0 (a-b+c) -2a

Question about my solution: Here can we say that z=1

now solving for last row:

(a-b+c)z=-2b -.a-b+c = -2b -> a+c=-b ->b=a+c


a+b+c = 0 ->a+c=-b -> a+c = -(a + c) so 0=0 Thus: infinitely many solutions when a+b+c = 0

and unique solution when a+b+c (not =) 0?

Marc N.

What is the original matrix/system?


Marc N.

Is the last entry -2a or is it -2b? You wrote -2a in the matrix, but -2b in your subsequent step.


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