 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/d/solution

x_{1} + x_{4} = 0

x_{2} - x_{4} = 0

, and

x_{3} + x_{4} = 0

x_{4} = t

x = t - 1 1 - 1 1 .

The displayed nonzero vector therefore forms a basis for the null space:

B_{null} = {(- 1, 1, - 1, 1)^{T}}, dim ker A = 1.

This agrees with the rank-nullity theorem: there are four columns and matrix rank three.

 New to topics? Read the docs here!