Why is Ax in col(A) if (A^T)Ax=0

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Thread starter horefaen
Start date Aug 15, 2009

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horefaen

Thread starter
Aug 15, 2009

Can someone explain why Ax is in col(A) if (A^T)Ax=0, A^T is the transpose.

Note: Ax is also orthogonal to col(A),(so x=0) so don't let that confuse you.

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Hurkyl

Staff Emeritus

Science Advisor

Gold Member

Aug 15, 2009

Isn't Ax always in col(A), no matter what A and x are?

horefaen

Aug 15, 2009

Yes it is, I know see it, I missed it, thank for your answer.

Why is Ax in col(A) if (A^T)Ax=0

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Standard formula for solving simultaneous equations of the form ax + by + c = 0

Ax+by=c is a straight line. When b=0 then it is // to y-axis