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Q.

If the system of equationsx+y+z=6,x+2y+λz=0,    x+2y+3z=10 has no solution, Thenλ=

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answer is 3.

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Detailed Solution

The augmented matrix AD=111612λ012310                                                           R3→R3-R2                                                    ~111612λ0003-λ10 Here rank AD=4 If the given system has no solution, then rankA≠rankAD ⇒3-λ=0 ⇒λ=3
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