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Question

If the system of linear equations
x+y+z=5x+2y+2z=6x+3y+λz=μ ,
(λ,μR), has infinitey many solutions, then the value of λ+μ is :

A
12
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B
10
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C
9
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D
7
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Solution

The correct option is B 10
D=∣ ∣11112213λ∣ ∣

C2C2C1, C3C3C1

=∣ ∣10011112λ1∣ ∣
=λ12

D1=∣ ∣511622μ3λ∣ ∣ =∣ ∣511400μ3λ∣ ∣=4λ12

D2=∣ ∣1511621μλ∣ ∣=λμ+4

Similaly, D3=μ7
For infinitely many solutions,
D=D1=D2=D3=0
λ=3,λμ=4,μ=7
λ+μ=10

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