NUMBER of soutions the equations have?

Question

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

Answer 1

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

Answer 2

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
 Answer is option 2

Answer 3

Consider the following system system of equations 

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

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

please open it -> http://www.geeksforgeeks.org/gate-gate-cs-2004-question-71/