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The number of non-trivial solutions of t...

The number of non-trivial solutions of the system `x=y+z=0, x+2y-z=0, 2x+y+3z=0`, is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
The given system of equations can be rewritten in matrix form as
`[(1,-1,1),(1,2,-1),(2,1,3)][(x),(y),(z)]=[(0),(0),(0)]` or `AX=B`
Now `|A|=1(6+1)+1(3+2)+1(1-4)` ltrbgt `=7+5-3=9!=0`
Since `|A|!=0`. So the given system of equations has only trivial solution. So, there is no -trivial solution.
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