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Question

Match the following

x+y+z=2

x+y+λz=1

x+μy+2y=3

(a) μ=1,λ=1 (i) No solution

(b) μ=2,λ=3 (ii) Unique Solution

(c) μ=1,λ=0 (iii) Infinite Solutions


A

a-ii; b – iii: c- ii

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B

a-i; b – ii: c- iii

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C

a-iii; b – iii: c- i

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D

a-i; b – iii: c- ii

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Solution

The correct option is B

a-i; b – ii: c- iii


Let’s convert A into Echelon form of

A = 11111λ1μ2

R3R3R1,R2R2R1 11100λ10μ11

R3R2 1110μ1100λ1

Let’s convert C into echelon form

C = 111211λ11μ23

R2R2R1, R3R3R1

111200λ110μ111

R2R3 11120μ11100λ11

When, μ=1, λ=1

Rank of A = 2, Rank of C = 3

No solutions possible

When, μ=2, λ=3

Rank of A = 3, Rank of C = 3 = Number of unknowns

unique solution

When, μ=1, λ=0

Rank of A = 2, Rank of C = 2

2 < Number of unknowns

Infinitie number of solutions.


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