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Question

If the system of equations 3x2y+z=0,λx14y+15z=0,x+2y3z=0 have non zero solution, then find λ

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Solution

Given system of equations
3x2y+z=0
λx14y+15z=0
x+2y3z=0 have non-zero solution
∣ ∣321λ1415123∣ ∣=0
3(4230)+2(3λ15)+1(2λ+14)=0
366λ30+2λ+14=0
4λ=20
λ=5

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