Please help me answer these question and provide a detailed visual step by step method. I will appreciate that alot :)

1. Find the rank of A, the nullity of A and the left nullity of A given the following information: 1 23 456 . . 001 -110 (a) The matrix A with row echelon form R = 000 010 000 001 (b) A 7 x 5 matrix A, such that the rank of AT = 4. S o O o T W 1 2. Find the left null space of B = ( 2 3 3. Let @ = (1,2,2,0) and 7 = (2, 3,3,5). (a) Find the cosine of the angle between # and . (b) Find projzv and the component of orthogonal to . 4. Find a basis for the orthogonal complement W+ if W = span{(1,4,5,0),(2,-1,2,1)}. Hint: Let A be a matrix such that row(A) = W. Then null(A) = W+