Menu Close

Let-A-and-B-are-matrices-in-R-2017-2017-such-that-A-1-A-B-1-B-1-and-det-A-1-2017-Find-det-B-




Question Number 55857 by Joel578 last updated on 05/Mar/19
Let A and B are matrices in R^(2017×2017)  such that   A^(−1)  = (A + B)^(−1)  − B^(−1)   and   det(A^(−1) ) = 2017  Find  det(B)
$$\mathrm{Let}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{matrices}\:\mathrm{in}\:\mathbb{R}^{\mathrm{2017}×\mathrm{2017}} \:\mathrm{such}\:\mathrm{that}\: \\ $$$${A}^{−\mathrm{1}} \:=\:\left({A}\:+\:{B}\right)^{−\mathrm{1}} \:−\:{B}^{−\mathrm{1}} \\ $$$$\mathrm{and}\: \\ $$$$\mathrm{det}\left({A}^{−\mathrm{1}} \right)\:=\:\mathrm{2017} \\ $$$$\mathrm{Find}\:\:\mathrm{det}\left({B}\right) \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *