Thread: Another set of matricies, but a different way of doing it.

1. Another set of matricies, but a different way of doing it.

Find the relationship between a,b, and c for which the system of equations will be consistent.

2x+y-z=a
x+2y+z=b
5x+4y-z=c

I need help for this, i can't seem to get the answer that the book has in the back which is, 2a+b-c=0. Can someone plzz help me solve this, or show me step by step on how to do this. Thanks!!

2. Originally Posted by snakeman11689
Find the relationship between a,b, and c for which the system of equations will be consistent.

2x+y-z=a
x+2y+z=b
5x+4y-z=c

I need help for this, i can't seem to get the answer that the book has in the back which is, 2a+b-c=0. Can someone plzz help me solve this, or show me step by step on how to do this. Thanks!!
augment your system in a matrix

$\displaystyle \begin{array}{ccc|c} 2 & 1 & -1 & a \\ 1 & 2 & 1 & b \\ 5 & 4 & -1 & c \\ \hline \end{array}$

now find the reduced row echelon of the 3x3 matrix, you will be able to see what conditions on a, b and c make the system consistent (chances are you get a row of zeros with 2a + b - c in the last entry, so that must be zero as well, try it!)