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#1 2007-04-07 17:25:47

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Proof

A set of equation


  For waht values of a does the system fail to have solutions, and for what values of a are there infinitely many solution.

Last edited by Stanley_Marsh (2007-04-07 17:26:23)


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#2 2007-04-07 17:34:17

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Proof

If the equations have infinite solution , then the two must be the same , transform them get


Then :

Get a=1 , Is this correct?

Last edited by Stanley_Marsh (2007-04-07 17:45:15)


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#3 2007-04-07 17:46:52

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Proof

If no solution


Get a=-1


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#4 2007-04-07 21:01:01

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Proof

Write

For there not to be a unique solution, the determinant of the matrix must be zero, i.e.

It’s a simple process to check that a = 1 gives infinitely many solutions while a = −1 gives no solutions.

Last edited by JaneFairfax (2007-04-07 21:06:51)

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#5 2007-04-07 21:09:50

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Proof

WoW , but I haven't learned about that


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