# The following system of linear equations   has  Option: 1 infinitely many solutions,  satisfying  Option: 2 infinitely many solutions,  satisfying  Option: 3 no solution Option: 4 only the trivial solution.

System of Homogeneous linear equations -

If ? ≠ 0, then x= 0, y = 0, z = 0 is the only solution of the above system. This solution is also known as a trivial solution.

If ? = 0, at least one of x, y and z are non-zero. This solution is called a non-trivial solution.

Explanation: using equation (ii) and (iii), we have

This is the condition for a system have Non-trivial solution.

-

so infinite non-trivial solution exist

now equation (1) + 3 equation (3)

10x - 20z = 0

x = 2z

Correct Option 2

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