Is it solvable?
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From: Biloxi, MS
Is it solvable?
In class, while reducing matrices in an augmented form, we came up with:
x + (13/2)z = 29/2
y + -(3/2)z = -9/2
No one could answer wether or not the system had a solution, and I still can not. He said if we came up with a concise answer as to wether or not the equations were solvable, he would give us a bonus point on the first test. So, any help would be appreciated. Thanks!~
x + (13/2)z = 29/2
y + -(3/2)z = -9/2
No one could answer wether or not the system had a solution, and I still can not. He said if we came up with a concise answer as to wether or not the equations were solvable, he would give us a bonus point on the first test. So, any help would be appreciated. Thanks!~
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From: Doh!!
Originally Posted by magician,Jan 28 2008, 10:43 AM
More accurately, the solution set is a line in 3-space. (A "graph" could be a line, a plane, a set of discrete points, a hyperbolic paraboloid, the interior of a cube, and so on.)
The coefficient matrix for the system is:
[1 0 13/2]
[0 1 -3/2]
and augmented matrix for this system is:
[1 0 13/2 29/2]
[0 1 -3/2 -9/2].
The dimension of the row space for the coefficient matrix is 2, as is the dimension of the row space for the augmented matrix; thus, the system is soluble. The dimension of the solution space is 3 - 2 = 1.
The solution space is the set of all points in 3-space having the form ((29 - 13t) / 2, (3t - 9) / 2, t), -∞ < t < ∞.
The coefficient matrix for the system is:
[1 0 13/2]
[0 1 -3/2]
and augmented matrix for this system is:
[1 0 13/2 29/2]
[0 1 -3/2 -9/2].
The dimension of the row space for the coefficient matrix is 2, as is the dimension of the row space for the augmented matrix; thus, the system is soluble. The dimension of the solution space is 3 - 2 = 1.
The solution space is the set of all points in 3-space having the form ((29 - 13t) / 2, (3t - 9) / 2, t), -∞ < t < ∞.
I got pwned.
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Regardless, we need to know what class you're taking. If you write down something similar to what magician posted, and such info is beyond the scope of your class, it will be evident that you asked for help on the inetrnets 
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From: Biloxi, MS
Business Cal, and yah I figured magician would come up with the answer, but I didn't want to rely just specifically on one person :-P.
Even while looking at his answer, I do think it's beyond what the teacher might be looking for :-P
Even while looking at his answer, I do think it's beyond what the teacher might be looking for :-P