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System of linear equations

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Question

Find the number of values of λ for which the homogeneous system of equations

               (aλ)x+by+cz=0

               bx+(cλ)y+az=0

               cx+ay+(bλ)z=0

has a non-trivial solution.

 

Difficult
Solution

Set determinant of the coefficient matrix equal to 0 to obtain a cubic equation.


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If the system of equations, ax+by+cz=0 , bx+cy+az=0  and cx+ay+bz=0  have non trivial solution, then


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