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Question

Number of solutions for the system of linear equations, x+y+z=6, x+2y+3z=14, and x+4y+2z=30 are


A
infinite
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B
unique
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C
zero
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Solution

The correct option is A infinite
Here, AX=B
111123147xyz=61430

Let's calculate |A|
|A|=1(1412)1(73)+1(42)=24+2=0
The given system of equations either has no solution or infinite number of solution.

Cofactor matricx of A is:
242363121

Adjoint of A is:
231462231
adj (AB)=231462231×61430
=000=0

We know that if |A|=0 and adj(AB)=0, then there exist infinite solutions.

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