Question 1050415
Determine the values for "a" for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. I need to solve using a matrix, and then row reducing. 
3X1 + aX2 + 6X3 = 6
-X1 + 3X2 - X3 = 1
2X1 - 2X2 + 6X3 = 11 
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You have to find the determinant of the "coefficient matrix"::
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D = (3*3*6 + (-1*2*6) + (2*-1*a) - [(6*3*2)+(-1*-2*3)+(6*-1*a))
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D = (54 - 12 - 2a - [36 + 6 - 6a])
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D = (42-2a)-(42-6a)
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D = 4a
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One unique solution if a is not zero
No solution when a = 0
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I'll leave the row reducing to you.
Cheers,
Stan H.
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