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Consider the following system system of equations

x_{1}-2x_{3}=0

x_{1}-x_{2}=0

2x_{1}-2x_{2}=0

- No solution
- Infinite number of solutions
- Three solution
- unique solution

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**.(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

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

x_{1}-2x_{3}=0 -> x1=2x_{3}

x_{1}-x_{2}=0 -> x_{1 }= x_{2}

2x_{1}-2x_{2}=0 -> x_{1 }= - x_{2}

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/