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The set of the all values of lamda for w...

The set of the all values of `lamda` for which the system of linear equations
`2x_(1) - 2x_(2) + x_(3) = lamdax_(1)`
`2x_(1) - 3x_(2) + 2x_(3) = lamda x_(2)`
`-x_(1) + 2x_(2) = lamda x_(3)` has a non-trivial solution,

A

is an empty set

B

is a singleton set

C

contains two elements

D

contains more than two elements

Text Solution

Verified by Experts

The correct Answer is:
3
System has non-initial solution
`:. |{:(lambda-2,,2,,-1),(2,,-3-lambda,,2),(-1,,2,,-lambda):}|=0`
`rArr (lambda -2)(3lambda +lambda^(2)-4)-2(-2lambda +2) -1(4-3-lambda)=0`
`rArr (lambda-2)(lambda-1)(lambda+4)+4(lambda-1)+(lambda-1)=0`
`rArr (lambda-1)(lambda^(2) +2lambda-8+5) =0`
`rArr (lambda-1)(lambda^(2) +2lambda-3)=0`
`rArr (lambda-1)^(2)(lambda+3)=0`
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