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URGENT HELP FURTHER MATHS (vECTOR SPACES) NEEDED

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sahrhp:
hey i got the first and second parts correct but i cannot get the correct answer by my strategy for the third part about the vector equation. PLEASE HELP ME .

ANSWERS TO THE FIRST TWO PARTS :

ans1.  DIM (range space)=3
ans2. basis of nullspace =(0, 1, -1, 1)

ans3. my strategy here was this:
 Using the fact that if vector(b) is a member of the column space of and matrix(H) then there exists a vector(r), a member of the rowspace(H) which is a solution to the equation Ar=b, is unique and the magnitude(r) is the least possible, I first proved that (2, -10, -1, -15) is a member of column space of H then proved that (1, -3, 1, -2) is a member of the rowspace of H and hence the magnitude(1, -3, 1, -2) should be the least possible.


but the answer is in correct and i have no clue of any other approach to this question. please to me how to solve and also, kindly point out the whats wrong with my approach. I would be really thankfull if you explain me what a range space is as i feel that its a gray area.

thank you so very much.

astarmathsandphysics:
I will try and answer it tomorrow.

sahrhp:
Thanks.

astarmathsandphysics:
ans=sqrt(2^2+(-10)^2+(-1)^2+(-15)^2)

sahrhp:
No the answer is sqrt(3) and i cant see how
plz help me ...
thanks

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