Matrices and Determinants 4 Question 15

16. The set of all values of λ for which the system of linear equations 2x12x2+x3=λx1,2x13x2+2x3=λx2 and x1+2x2=λx3 has a non-trivial solution

(2015 Main)

(a) is an empty set

(b) is a singleton set

(c) contains two elements

(d) contains more than two elements

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Answer:

Correct Answer: 16. (c)

Solution:

  1. Given system of linear equations

2x12x2+x3=λx1(2λ)x12x2+x3=02x13x2+2x3=λx22x1(3+λ)x2+2x3=0x1+2x2=λx3x1+2x2λx3=0

Since, the system has non-trivial solution.

2λ212(3+λ)2=0λλ

Hence, λ contains two elements.



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