Question: Using the matrix identity det(Ik ab) = 1 ba, where a and b are column vectors of dimension k, prove (8.27). Hint: Use

Using the matrix identity det(Ik − ab) = 1 − ba, where a and b are column vectors of dimension k, prove (8.27). Hint: Use a = xi and b = x

i(XX)−1 and the fact that det[X

(i)X(i)] =det[{Ik −

xix

i(XX)−1}XX].

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