# NUMBER of soutions the equations have?

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Consider the following system system of equations
x1-2x3=0
x1-x2=0
2x1-2x2=0

1.   No solution
2.  Infinite number of solutions
3.  Three solution
4. unique solution

rank of matrix is less than n(3<2).....take any variable as orbitory value....(infinite no of solution)

Coefficents matrix
A= | 1   0   -2   |
|  1  -1    0  |
|  2   -2   0  |
Homogenous equation has 0 as trivial solution .hence option 1 is wrong

Now the rank of A < 3 as 2nd and 3rd row is proportional .
Hence the equations have infinite no of solution

Consider the following system system of equations

x1-2x3=0         ->      x1=2x3
x1-x2=0           ->      x= x2
2x1-2x2=0       ->      x= - x2

Here every variable take more than 2 value Thus system have infinite  solution.

## Related questions

1
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My solution:- Since the Determinant of matrix is Zero. So it will posses non trivial solution. Now what should be the answer ? According to me Option D as rank is < Order so infinite number of solutions
The system of simultaneous equations $x+2y+z=6\\2x+y+2z=6\\x+y+z=5$ has unique solution. infinite number of solutions. no solution. exactly two solutions.