# Find all values of \lambda for which the homogeneous linear system (\lambda -2) x + y = 0...

## Question:

Find all values of {eq}\lambda {/eq} for which the homogeneous linear system

{eq}(\lambda -2) x + y = 0 \\ x + (\lambda -2) y = 0 {/eq}

has non trivial solutions.

## Homogeneous Linear System:

Given the homogeneous linear system

{eq}(\lambda -2) x + y = 0 \\ x + (\lambda -2) y = 0 {/eq}

the values of parameter {eq}\lambda {/eq} for which the system has no trivial solutions are found by

setting to zero the determinant of the coefficient matrix, i.e.

{eq}(\lambda -2)^2 - 1 =0 {/eq}

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