 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2005/calculus-linear-algebra-discrete-mathematics-logic-and-proof-and-models-of-computation/1/d/solution

Here

v_{3} = 2 v_{1} - v_{2}

v_{1}, v_{2}

a v_{1} + b v_{2} = 0

, the

e_{1}

and

e_{2}

coordinates give

a + b = 0

and

a - b = 0

, hence

a = b = 0

3 - 2 = 1

rank α = 2, nullity α = 1.

More explicitly, the relation

- 2 v_{1} + v_{2} + v_{3} = 0

ker α = span {- 2 e_{1} + e_{2} + e_{3}} .

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