SOLUTION: find the value of "a" and "b" so that the system of the of equation 2x+3y+5z=9 7x+3y-2z=8 2x+3y+az=b has 1)no solution 2)a unique solution 3)an infinite

Algebra ->  Matrices-and-determiminant -> SOLUTION: find the value of "a" and "b" so that the system of the of equation 2x+3y+5z=9 7x+3y-2z=8 2x+3y+az=b has 1)no solution 2)a unique solution 3)an infinite      Log On


   

Question 111687: find the value of "a" and "b" so that the system of the of equation
2x+3y+5z=9
7x+3y-2z=8
2x+3y+az=b has
1)no solution
2)a unique solution
3)an infinite number of solution
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the value of "a" and "b" so that the system of the of equation
2x+3y+5z=9
7x+3y-2z=8
2x+3y+az=b has
-----------------------
1)no solution
Find the determinant of the "coefficient matrix".
Let that determinant be zero.
Solve for "a".
I get a=5
--------------------
2)a unique solution
There will be a unique solution as long
as a is not 5; b may be any value
----------------------------
3)an infinite number of solution
Cause the 3rd equation to be a multiple of the 2nd equation.
Multiply thru the 3rd equation by (7/2) to find (7/2)a=-2
and (7/2)b=16/7
Then solve for and b.
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Cheers,
Stan H.