a 4*4 matrix A= (1234), (2345),(3456),(4567), find the rand and the distance between v=(1 0 0 0) and ker(A)? need help to solve pls

Question

a 4*4 matrix A= (1234), (2345),(3456),(4567), find the rand and the distance between v=(1 0 0 0) and ker(A)?  need help to solve pls

anonymous · Answer

Are those the rows or the columns?

anonymous · Answer

rows

anonymous · Answer

Rank=2

anonymous · Answer

can you show me how to find the rank?

kinggeorge · Answer

rref the matrix, so that you have the longest diagonal of ones possible. However many rows have a one in that diagonal, is your rank.

anonymous · Answer

ok i got the rank but how to find the distance between v and ker(A)?

kinggeorge · Answer

My previous answer was slightly incorrect. Just rref it so that each row has a one at the start. However many rows start with a one is your rank. All the other rows should consist of only 0's

anonymous · Answer

yah the rank = the #of nonzero row in rref

kinggeorge · Answer

exactly. have you found the ker(A) yet?

anonymous · Answer

no but juz solving Ax=0 rite?

anonymous · Answer

correct

kinggeorge · Answer

yes

anonymous · Answer

so i hv kerA= (1 -2 1 0) , (2 -3 0 1) in columns

anonymous · Answer

need help to find the distance

anonymous · Answer

To be honest I'm not really sure what they mean by distance. Since any basis for the kernel in this case will span a plane and the vector is a line that is either parallel to or intersects the plane. Angle seems reasonable but I don't know about distance.

anonymous · Answer

*vector spans a line

anonymous · Answer

but on my assignment it really ask to find the distance between v and the ker (A)

kinggeorge · Answer

is there any more information given in the problem?

anonymous · Answer

no juz the matrix and question as i mentioned , but the matrix is symmtric

kinggeorge · Answer

I'm with Alchemista here. Having the distance between Ker(A) and v doesn't make much sense.

anonymous · Answer

maybe i need to ask my prof .. thx you guys anyways