 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof-resit/4/c/ii/solution

The system is consistent for every $b \in R^{m}$ : take

x = Yb

, since

A (Yb) = (A Y) b = b

. Thus

Y

is a right inverse giving an explicit solution for every right-hand side.

All solutions are

Yb + u

with

u

in the kernel of a linear map represented by

A

n - m

; the solution is unique when

n = m

, and is nonunique when

n > m

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