Question

I Let A = 2 4 20 -2-5 7 3 -37-86 suppose it is found that the RREF of A is [ 109.17 01-54 -oooo find a basis for the hull spare of A find a basis for the column space of A find a basis for the Row space of A

Answer 1

Let A= 2 -2 0 -2 3 4 -5 7 7 -8 3 6 Suppose it is found that RR EF of A is 1 g 17 1 5 -4 1.) Find a basis for the null space of A Any is Null space of a Matrix: solution of system Axzo is Null space of Matrix. Ax=0 We know that Äx=0 also same where À is Reduced Row echlon form (RREF) BLA. hence 1 O 17 -5 1 -4 Hz e oooo O M3 G ng MA 11, +9₂ + 170 = 0 Na 5 Hz - 4 H=0

Now let Two equation and four variables Hz and no are free variable let Hz = StER and na = t hence H1 = gs-17 t H₂ = 5 st 4 t -gs-17t =) X= 17 ип 5 st 4 t t Az S N4 т hence Basis of Null space 9 -17 1 2.) Find a basis for the column space of A. Angin RREF 1 0 g 17 1 - 5 4 O here Prout element in RREF is column first and secondo

So corresponding to these columm, in our origual Matrix's calumm form a basis of columm space. hence Basis of columm space 4 2 - 2 3 5 ㅋ 3.) Find a basis for the Row space of A. Any: :RREF 11 O 9 -5 17. -4 O here in RREF Pivot Columin Row first and Second So Basis of Row space is these two Row. = Basis of Row Space = 1 -5 9