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Question

The following set of equations has

3x + 2y + z = 4

x - y + z = 2

-2x + 2z = 5

A
No solution
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B
A unique solution
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C
Multiple solutions
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D
An inconsistency
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Solution

The correct option is B A unique solution
Using R1R2

[A : B] = 111:2321:4202:5

R1R23R1

R3R32R2

- 111:2052:2024:9

R3R3+25R2

- ⎢ ⎢111:2052:202165:415⎥ ⎥

ρ(A) = ρl [A : B] = 3 = Number of unknowns

\(\\therefore ) Unique solution.

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