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**1. Homework Statement**

Find a necessary condition for the three planes given below to have a line of intersection.

-x +ay+bz=0

ax-y+cz=0

bx+cy-z=0

**2. Homework Equations**

in order to get a line of intersection between the planes..i know i need one line of the matrix to be [0 0 0|0]

**3. The Attempt at a Solution**

well heres the attempt..and its wrong

[ -1 a b | 0

a -1 c | 0

b c -1| 0 ]

=>

[-1 a b | 0

0 (a^2-1) ba+c | 0 (aRow1 + Row2)

0 (ab+c) b^2+1 | 0 ] (brow1 + Row 2)

=>

[ -1 a b | 0

0 a^2 -1 ba+c |0

0 0 2abc +c^2 - a^2 + b^2 +1) |0 ] (ab+c row2- a^2-1 Row1)

then what i did ..by inspection i made 2abc+c^2 -a^2 +b^2 +1 = 0 by letting a=b=1, and c=-1......

but that doesnt work becasue that owuld make plane 1 and 2 the same plane.

i need help

thanks

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