Matrices and Determinants 4 Question 31

32. For what value of k, does the following system of equations possess a non-trivial solution over the set of rationals x+y2z=0,2x3y+z=0, and x5y+4z=k

Find all the solutions.

(1979,3M)

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Answer:

Correct Answer: 32. (9)

Solution:

  1. Since, the given system of equations posses non-trivial solution, if |012031k54|=0k=0

On solving the equations x=y=z=λ

[say]

For k=0, the system has infinite solutions of λR.



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