 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/18/d/solution

Using the signs chosen above, explicit multiplication gives

A v_{1} = \frac{1}{2} (11) = u_{1}, A v_{2} = (1 - 1) = 2 u_{2}, A v_{3} = 0 .

Thus the nonzero cases obey

A v_{m} = σ_{m} u_{m}

U = (u_{1} u_{2})

and

V = (v_{1} v_{2} v_{3})

, then

A = U Σ V^{T}

with

Σ = (100200)

 New to topics? Read the docs here!