 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof-resit/6/b/solution

Denote the five rows by

r_{1}, \dots, r_{5}

. They satisfy

r_{1} = r_{2} + r_{4}, r_{5} = r_{2} + r_{4} - r_{3} .

Thus

r_{2}, r_{3}, r_{4}

α r_{2} + β r_{3} + γ r_{4} = 0

, coordinate 1 gives

α = 0

, coordinate 2 then gives

β = 0

, and coordinate 4 gives

γ = 0

. Therefore

B_{row} = {(1, 1, 0, 0), (0, 1, 1, 0), (0, 0, 1, 1)}, rank A = 3.

As an alternative basis, the nonzero rows of the reduced row echelon form are

rref (A) = 100000100000100 1 - 1 100 .

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