AP EAPCET 25-Aug-2021 Shift 2 Paper

To Find The number of solutions of the following system of linear homogeneous equations
x−y+z=0 ...(i)
x+2y−z=0 ...(ii)
2x+y+3z=0 ...(iii)
We can write above equations in matrix form i.e.
[

1	−1	1
1	2	−1
2	1	3

][

x

y

z

]=0
or AX=0, where A=[

1	−1	1
1	2	−1
2	1	3

]
Since, we know that, if |A|=0, then only non-trivial solution exist.
Consider, |A|=[

1	−1	1
1	2	−1
2	1	3

]
∴ |A|=1[2×3−(−1)]+1[3+2]+1[1−4]
=7+5−3=9≠0
∵ |A|≠0
Hence, there is no non-trivial solutions.
⇒ There will be only l trivial solution.