SATHEE: Matrices and Determinants 4 Question 24

Matrices and Determinants 4 Question 24

25. The system of equations $λ x + y + z = 0, - x + λ y + z = 0$ and $- x - y + λ z = 0$ will have a non-zero solution, if real values of $λ$ are given by …

(1982, 2M)

Analytical and Descriptive Questions

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Answer:

Correct Answer: 25. $λ = 0$

Solution:

Given system $λ x + y + z = 0, - x + λ y + z = 0$

and $- x - y + λ z = 0$

will have non-zero solution, if

$| \begin{array}{ccc} λ & 1 & 1 \\ - 1 & λ & 1 \\ - 1 & - 1 & λ \end{array} | = 0$

$\Rightarrow λ (λ^{2} + 1) - 1 (- λ + 1) + 1 (1 + λ) = 0$

$\Rightarrow λ^{3} + λ + λ - 1 + 1 + λ = 0$

$\Rightarrow λ^{3} + 3 λ = 0$

$\Rightarrow λ (λ^{2} + 3) = 0 \Rightarrow λ = 0$

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Matrices and Determinants 4 Question 24

25. The system of equations λx+y+z=0,−x+λy+z=0 and −x−y+λz=0 will have a non-zero solution, if real values of λ are given by …

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25. The system of equations $λ x + y + z = 0, - x + λ y + z = 0$ and $- x - y + λ z = 0$ will have a non-zero solution, if real values of $λ$ are given by …