Q. Consider the system of equations :
x + ay = 0, y + az = 0 and z + ax = 0. Then the set of all real values of ‘a’ for which the system has a unique solution is:

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Solution:

Given system of equations is homogeneous which is



It can be written in matrix form as

Now,
So, system has only trivial solution.
Now, | A | = 0 only when a = - 1
So, system of equations has infinitely many solutions which is not possible because it is given that system has a unique solution.
Hence set of all real values of ‘a’ is R - {- 1}.