Question 34

The system of linear equations
$$x + y + kz = 1$$
$$x + ky + z = 1$$
$$kx + y + z = 1$$
has

Solution

The system will have a unique solution if x=y=z

Substituting in 1, we get x+x+kx=1 => x(2+k) =1

=> x = 1/2+k = y = z, where k is not equal to -2

Hence it has a unique solution for infinitely many choices of k

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