System of linear equations

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Question

Find the number of values of $λ$ for which the homogeneous system of equations
                $(a - λ) x + b y + c z = 0$
                $b x + (c - λ) y + a z = 0$
                $c x + a y + (b - λ) z = 0$
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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System of linear equations

Unlock the full solution & master the concept.

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.

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

Ready to Test Your Skills?

free study material

Find the number of values of $λ$ for which the homogeneous system of equations
$(a - λ) x + b y + c z = 0$
$b x + (c - λ) y + a z = 0$
$c x + a y + (b - λ) z = 0$
has a non-trivial solution.