Let T:R4→R3T: \mathbb{R}^4 \to \mathbb{R}^3T:R4→R3 be defined by T(x,y,z,w)=(x+y,y+z,z+w)T(x, y, z, w) = (x + y, y + z, z + w)T(x,y,z,w)=(x+y,y+z,z+w). By the Rank-Nullity Theorem, what is dim(ker(T))\dim(\ker(T))dim(ker(T))?
dim(ker(T))=0\dim(\ker(T)) = 0dim(ker(T))=0
dim(ker(T))=1\dim(\ker(T)) = 1dim(ker(T))=1
dim(ker(T))=2\dim(\ker(T)) = 2dim(ker(T))=2
dim(ker(T))=3\dim(\ker(T)) = 3dim(ker(T))=3