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Question

Mathematics Question on Matrices

The system of linear equations : x+y+z=0,2x+yz=0,3x+2y=0x + y + z = 0, 2x + y - z = 0, 3x + 2y = 0 has :

A

no solution

B

a unique solution

C

an infinitely many solution

D

None of these

Answer

an infinitely many solution

Explanation

Solution

The system is homogenuous system.
\therefore it has either unique solution or infinitemany solution depend on A|A|
A=111 211 320\therefore \left|A\right|=\begin{vmatrix}1&1&1\\\ 2&1&-1\\\ 3&2&0\end{vmatrix}
=23+1=0=2-3+1=0