For which value of andlambda;will the following equations fail to have unique solution?3x andndash; y + andlambda;z = 12x + y + z = 2x + 2y andndash; andlambda;z = andndash;1Correct answer is '-3.5'. Can you explain this answer?

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For which value of λ will the following equations fail to have unique solution?

3x – y + λz = 1
2x + y + z = 2
x + 2y – λz = –1

Correct answer is '-3.5'. Can you explain this answer?

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For which value of λwill the following equations fail to have u...

The matrix form of the given system of equations is

The given system of equations will have a unique solution if and only if the coefficient matrix is non singular.

Performing

we get

Performing

we get

Therefore, the coefficient matrix will be non-singular if and only if

i.e., if and only if

Thus, the given system will have a unique solution if

In case of

the equation (1) becomes

Performing

we get

showing that given equations are inconsistent in this case.

Thus if

no solution exists.

The correct answer is: -3.5

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For which value of λwill the following equations fail to have unique solution?3x – y + λz = 12x + y + z = 2x + 2y – λz = –1Correct answer is '-3.5'. Can you explain this answer?

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