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.
