 Solution

ID: past-exam-of-the-algebra-1-and-differential-equations-1-course-of-the-university-of-oxford/2014/3/a/i/solution

The rank-nullity theorem states that for a linear map

A : X \to Y

dim X = dim ker A + dim im A .

Equivalently, nullity plus rank equals the dimension of the domain. One proof extends a basis of

ker A

to a basis of

X

; the images of the added vectors form a basis of

im A

 New to topics? Read the docs here!