# Solution: 2015-17 Inverse of a minor

Let $$H$$ be an $$N \times N$$ positive definite matrix and $$G = H^{-1}$$. Let $$H’$$ be an $$(N-1) \times (N-1)$$ matrix obtained by removing the $$N$$-th row and the column of $$H$$, i.e., $$H’_{ij} = H_{ij}$$ for any $$i, j = 1, 2, \cdots, N-1$$. Let $$G’ = (H’)^{-1}$$. Prove that
$G_{ij} – G’_{ij} = \frac{G_{iN} G_{Nj}}{G_{NN}}$
for any $$i, j = 1, 2, \cdots, N-1$$.

The best solution was submitted by Park, Hun Min (박훈민, 수리과학과 2013학번). Congratulations!

Here is his solution of problem_2015_17.

Alternative solutions were submitted by 이종원 (수리과학과 2014학번, +3), 최인혁 (2015학번, +3), 박성혁 (수리과학과 2014학번, +3, solution), 신준형 (2015학번, +3), 이영민 (수리과학과 2012학번, +3), 장기정 (수리과학과 2014학번, +3), 함도규 (2015학번, +3).

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