 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-i/2/a/i/solution

T_{A}

im T_{A} = {A x : x \in R^{m}} .

Consequently

b \in im T_{A}

means exactly that some

x \in R^{m}

satisfies

A x = b

. This is precisely the existence of a solution of the linear system.

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