Another linear algebra trouble with matricies

M

mlane

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Sep 6, 2005
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I have a sysem of two equations.
I am suppose to find an incosistant solution,
a uniqe solution, and many solutions, but it does not make sense to me.
I have the system
1 3 2
3 h k

I took Row 1 * -3 +R2 I get

1 3 2
0 h-9 k-6

So I divide row 2 by h-9 and get

1 3 2
0 1 k-6/h-9

multiply row two by -3 +Row 1 for new Row 1 I get

1 0 2+3(k-6)/h-9
0 1 k-6/h-9

How do I get the solutions for these? Do I set x1 and x2 to zero? I know if h=9 the solution gives a divide by zero error. I believe this is the inconsistent portion but I am not sure about the other two.
 
Please post the actual system of equations.
 
the original equations are
X1 + 3X2 = 2
3X1 + hX2 = k

I put these in matrix form to help solve.

I don't know how to subscript the 1 and 2 with this system.
 
The matrix of coefficients has a determinate of h-9.
Thus for any h not equal to 9 we get a solution for any value of k.
If h=9 and k=6 we get a line with infinitely many solutions.
If h=9 and k not equal to 6 we get an inconstant system.
 
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