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Is the trivial solution is always a unique solution? True or false????

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masterpiece11 | Student | Salutatorian

Posted March 7, 2013 at 7:35 AM via web

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Is the trivial solution is always a unique solution? True or false????

Tagged with linear algebra 1, math

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pramodpandey | College Teacher | Valedictorian

Posted March 28, 2013 at 9:43 AM (Answer #2)

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Let us consider the system of equation

2x+3y = 0

4x+6y =0

In this system of equation , x=y=0 is trivial solution.

But this solution is not unique as well.

Since one equation is multiple of the other so ,

2x+3y=0

has infinite no. of solution.

Thus we can conclude that trivial solution is always not unique.

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pramodpandey | College Teacher | Valedictorian

Posted March 13, 2013 at 12:41 PM (Answer #1)

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False

Homogeneous system - may be unique.

Non Homogeneous system  not unique.

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