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The greatest value of for which the sy...

The greatest value of for which the system of linear equations
`x-cy-cz=0`
`cx-y+cz=0`
`cx+cy-z=0`
Has a non-trivial solution, is `1/k`. The value of k is _________.

Text Solution

Verified by Experts

The correct Answer is:
B
`x-cy-cz=0`
cx-y+cz=0`
cx+cy-z=0`
`:'D_x=D_y=D_z=0" " :.` For non trivial solutions
D=0
`D=|{:(1,-c,-c),(c,-1,c),(c,c,1):}|=1(1-c^2)+c(-c-c^2)-c(c^2+c)`
`=1-c^2-c^2-c^3-c^3-c^2`
`=1-2c^(3)-3c^(2)+1=0`
`2c^3+3c^2-1=0`
`implies(2c-1)^2=0,c=-1,-1,1//2`
`:.` Greatest value of 'c' is 1/2.
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