Let A=

Give a one-to-one parameterization of the ker(A)

Would it just be

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- Oct 20th 2009, 04:58 PMZockenOne-to-one parameterization
Let A=

Give a one-to-one parameterization of the ker(A)

Would it just be - Oct 20th 2009, 06:15 PMJose27
How about

- Oct 20th 2009, 06:36 PMZocken
Thanks Jose, may I ask how you got that answer??

- Oct 20th 2009, 06:45 PMJose27
Notice that iff . If then we get three equations that are exactly the same . So given any values for and is completely determined (i.e. has dimension 2).

- Oct 20th 2009, 07:16 PMhjortur
If you multiply a general vector (on the right side!) v=(x,y,z)' with the given matrix,

you will end up with the vector (x+y+z,x+y+z,x+y+z)' <-- (transposed).

Now if A reprisents a linear map h:V->W. Then ker(A) corresponds to the

subspace which image under h is 0.

Now what that means is what does v=(x,y,z) have to be so that when you multiply it

with A you get 0? - Oct 20th 2009, 07:29 PMZockenQuote:

Now what that means is what does v=(x,y,z) have to be so that when you multiply it

with A you get 0?

- Oct 21st 2009, 04:42 AMhjortur
- Oct 26th 2009, 05:24 PMZocken
One last question...Let b=Ae1. Find a one to one parameterization of the solution set Ax=b.

Would this makes sense using the above answer?

- Oct 27th 2009, 04:57 AMhjortur
Yes, that is correct.

The solution describes a plane with normal vector (1,1,1) going through the point e1.

So the function is not one-to-one , because all the points on that plane will go to b.