Match the following for system of linear equations
2x -3y + 5z =12 3x+y+λz=μ
x -7y + 8z =17 Column - IColumn - I(P)Unique solution(1)λ=2,μ=7(Q)Infinite solution(2)λ≠2,μ=7(R)No solution(3)λ≠2,μ≠7(S)Consistent system(4)λ∈R,μ≠7equation(5)λ=2,μ≠7
A
P→2;Q→1;R→5;S→1,2
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B
P→2,3;Q→1;R→5;S→1,2,3
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C
P→2,3;Q→1;R→4,5;S→1,2,3
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D
P→3;Q→1;R→4,5;S→2,3
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Solution
The correct option is BP→2,3;Q→1;R→5;S→1,2,3 D=∣∣
∣∣2−3531λ1−78∣∣
∣∣=88−110+11λ=(11λ−22) D1=∣∣
∣∣12−35μ1λ17−79∣∣
∣∣=33λ=11μ+1=11(3λ−μ+1) D2=∣∣
∣∣21253μλ1178∣∣
∣∣=11μ−22λ−33=11(μ−2λ−3) D3=∣∣
∣∣2−31231μ1−717∣∣
∣∣=11(μ−7)
For unique solve →D≠0 λ≠2,μ∈R
For infinte solution, D=0,D1=0,D2=0,D3=0 λ=2,3λ−μ+1=0,μ−2λ−3=0 μ=7
So λ=2&μ=7
For no solution →λ=2,μ≠7
Unique solution and infinite solution make consistent system.