 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2014-resit/3/iii/solution

Scaling the whole matrix scales all

n

rows. The multilinearity of the determinant therefore gives

det (c A) = c^{n} det A .

This includes

c = 0

for

n \geq 1

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