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Question

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)λ2,μ=7(R)No solution(3)λ2,μ7(S)Consistent system(4)λR,μ7equation(5)λ=2,μ7

A
P2;Q1;R5;S1,2
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B
P2,3;Q1;R5;S1,2,3
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C
P2,3;Q1;R4,5;S1,2,3
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D
P3;Q1;R4,5;S2,3
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Solution

The correct option is B P2,3;Q1;R5;S1,2,3
D=∣ ∣23531λ178∣ ∣=88110+11λ=(11λ22)
D1=∣ ∣1235μ1λ1779∣ ∣=33λ=11μ+1=11(3λμ+1)
D2=∣ ∣21253μλ1178∣ ∣=11μ22λ33=11(μ2λ3)
D3=∣ ∣231231μ1717∣ ∣=11(μ7)
For unique solve D0
λ2,μR
For infinte solution, D=0,D1=0,D2=0,D3=0
λ=2,3λμ+1=0,μ2λ3=0
μ=7
So λ=2&μ=7
For no solution λ=2,μ7
Unique solution and infinite solution make consistent system.



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