# Inconsistency matrix question...

• May 3rd 2013, 12:17 AM
rodders
Inconsistency matrix question...
Ok.. Have a look at this problem and then look at the second post:

http://i41.tinypic.com/73f29t.jpg
• May 3rd 2013, 12:23 AM
rodders
Re: Inconsistency matrix question...
Can anyone explain the second examiners solution? I understand the first and third approach but what is happening in the second method below, In particular what does trianglex, triangle y , trianglez mean in the second line of the solution i have circled in red?

http://i41.tinypic.com/23mvp7k.jpg
• May 4th 2013, 11:42 AM
HallsofIvy
Re: Inconsistency matrix question...
The "\$\displaystyle \Delta\$" is, of course the determinant. Since that is 0 it follows that there cannot be a unique solution. But I think when they say "Showig \$\displaystyle \Delta= 0\$ and thinking this is it" they the mean that alone does NOT show that the system is inconsistent- there might be an infinite number of solutions. I do think that "and \$\displaystyle \Delta_x\$, \$\displaystyle \Delta_y\$, \$\displaystyle \Delta_z\$= 0" is misleading. In order to have the system inconsistent, you must show that \$\displaystyle \Delta= 0\$ and that at least one of \$\displaystyle \Delta_x\$, \$\displaystyle \Delta_y\$, \$\displaystyle \Delta_z\$ is NOT 0.

I am rather disappointed that the most direct demonstration is not given:

If you add the second and third equations, the "y" and "-y" terms cancel leaving 11x+ 11z= 37.

Multiplying the second equation by 2 gives 6x+ 2y- 8z= 14 and adding the first equation to that gives 7x+ 7z= 14. Do you see why those two equations are impossible?
• May 4th 2013, 10:12 PM
rodders
Re: Inconsistency matrix question...
Sorry but i still don't know what Det(x), det(y), det(z) actually mean? I know how to work out the det of matrix but never come across det(x) etc?
How do you actually work that out of a matrix?