Q.

Find the number of values of λ for which the homogeneous system of equations               (a−λ)x+by+cz=0               bx+(c−λ)y+az=0               cx+ay+(b−λ)z=0has a non-trivial solution.

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answer is 3.

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Detailed Solution

Set determinant of the coefficient matrix equal to 0 to obtain a cubic equation.
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Find the number of values of λ for which the homogeneous system of equations               (a−λ)x+by+cz=0               bx+(c−λ)y+az=0               cx+ay+(b−λ)z=0has a non-trivial solution.