 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/digital-systems-linear-algebra-introduction-to-formal-proof/4/d/solution

A x = b

has a solution, the multiplication identity from part (c) expresses

b

b \in Col (A)

Conversely, if

b

x_{1}, x_{2}, x_{3}

with

b = x_{1} a_{1} + x_{2} a_{2} + x_{3} a_{3}

. Put those scalars into the column vector

x

. Then

A x = b

. This proves both directions of the claimed equivalence.

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