Q.

If the system of linear equations x+y+z=6,x+2y+3z=10,3x+2y+λz=μ has more than two solutions, then λ3+μ3=

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answer is 2745.

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Detailed Solution

Augmented matrix =113     11623102λμ apply R2→R2−R1, R3→R3−3R1                                      ~111601240-1λ-3μ-18 apply R3→R3+R2~1116012400λ-1μ-14The system has more than 2 solutions.⇒λ-1=0, μ-14=0⇒λ=1, μ=14∴λ2+μ3=13+143=2745
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