A=[ 7 8 -2 -6 7 4 1 ; 2 4 -4 -13 9 9 -12 ; 6 6 0 -9 8 9 -4 ; 1 8-14 -22 5 8 -1 ; 4 9 -10 -14 7 4 -1]
B=[ 19 4 4 14 -3 -7 -5 ; 21 -6 -5 10 14 -2 4 ; 22 -4 5 13 5 -6 4; 41 20 0 26 11 -1 -27 ; 29 14 -2 20 3 -4 -19]
Remark: You may only use rref , or commands that are covered inour MATLAB guides, and no other special MATLAB functions for thisproblem.
(a) (3 points) Find a basis for Col(A) and determine itsdimension.
(b) (5 points) Find a basis for Nul(A) and determine itsdimension.
(c) (3 points) Find a basis for Row(A) and determine itsdimension.
(d) (5 points) Find a basis for the left nullspace of A anddetermine its dimension.
(e) (2 points) Find a basis for Col(B) and determine itsdimension.
(f) (6 points) Determine whether Col(A) = Col(B), i.e. determinewhether the two given subspaces of R 5 are the same or not. If not,find a vector v
that belongs in one of the subspaces and not the other.
(g) (6 points) Determine whether Nul(A) = Nul(B). If not, find avector v that belongs in one of the subspaces and not theother.
