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If the system of equations 3x-2y+z=0, la...

If the system of equations `3x-2y+z=0, lambda x-14y+15z=0, x+2y+3z=0` have a non trivial solution, then the value of `lambda^(2)` must be

Text Solution

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The correct Answer is:
841
`|(3,-2,1),(lambda,-14,15),(1,2,3)|=0`
`rArr 3(-42-30) +2 (3lambda-15)+1(2 lambda+14)=0 rArr8 lambda=232`
`therefore lambda=29 " "rArr lambda^(2) =29^2 =841`
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