 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/digital-systems-linear-algebra-introduction-to-formal-proof/5/c/iii/solution

T : V \to W

is onto, or surjective, when every

w \in W

equals

T (v)

for some

v \in V

; equivalently its image is all of

W

. Here $T$ is not onto, because its image has dimension two while its declared codomain

R^{3}

has dimension three. Indeed every image vector satisfies

x + y - 3 z = 0

, so, for example,

(0, 0, 1)

is not attained.

 New to topics? Read the docs here!