In: Advanced Math
Find the kernel (or nullspace) and the image of each linear map together with their basis.
(a) T :R4 →R3 given by f(x,y,z,w)=(3x+y−3z+3w , x+y+z+w , 2x+y−z+2w)
(b) T :R3 →R5 given by f(x,y,z)=(2x−y+6z , x−y−z , x+y−5z , z−y , −x+2z)
c) T :R4 →R3 given by f(x,y,z,w)=(x−y−3z+w , 2x−3y+z+2w , 3x+y−4z−w)