 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2/1/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

y \neq = 0

, the equation would imply

b = - (x / y) a

, contradicting the assumed nonparallel directions. Hence

y = 0

. Then

x a = 0

and

a \neq = 0

x = 0

. This proves that the two vectors are linearly independent.

 New to topics? Read the docs here!