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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
in Linear Algebra 177 views

3 Answers

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

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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
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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.

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

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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
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