Can someone help me with this matrix?

Question

anonymous · Answer

attachment

anonymous · Answer

I find the for the null space to:

anonymous · Answer

I need some help to the rank and nullity for the null space

uri · Answer

I know this but i don't know how to solve it here,i'ts pretty long.

anonymous · Answer

@amistre64 Can you help me with this matrix?

amistre64 · Answer

you need help with elementary row operations?  or organizing it afterwards?

anonymous · Answer

I think I have found the basis for the null space (see #2)

But I cant find the rank and nullity for null space..

amistre64 · Answer

x1  x2  x3      x4
 1    1    0       0 
 0    0    1    -1/2
 0    0    0       0
       ^             ^
       free variables

x1 = x2(-1) + x4(  0  )
x2 = x2(  1) + x4(  0  )
x3 = x2(  0) + x4 (1/2)
x4 = x2(  0) + x4(  1 )


so our basis for the nulspace is a 2x4 matrix

amistre64 · Answer

nullityA is the number of free variables
rankA is the rest of it

amistre64 · Answer

2 free variables
2 remaining ..

whats this tell us

anonymous · Answer

So the rank is 2 and nullity is 2

amistre64 · Answer

correct

anonymous · Answer

Then I had done it correctly. :)

amistre64 · Answer

you did fine :)

anonymous · Answer

What confused me was:
Find the rank, the nullity and a basis "for the null space" of the matrix

anonymous · Answer

So it is not the rank and the nullity for the null space I should find..