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 November 3rd, 2015, 08:46 AM #1 Newbie   Joined: Nov 2015 From: Hungary Posts: 1 Thanks: 0 Det. of an n x n matrix, pls help to solve this problem My task is to prove if it's true that: a.) det( A^2 + A + I(n) )>=0 b.) det( I(n) + A + B + A^2 +B^2) >= 0 if A and B are n x n matrices and A,B(i,j) takes the values from R (set of real numbers) and I(n) it's an n x n Identity matrix * >= means equal or higher Thanks  December 27th, 2015, 02:34 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 `Hint: $\displaystyle A^2+ A+ I= A^2+ A+ \frac{1}{4}I+ \frac{3}{4}I= (A+ \frac{1}{2}I)^2+ \frac{3}{4}I$ $\displaystyle A^2+ B^2+ A+ B+ I= A^2+ A+ \frac{1}{4}I+ B^2+ B+ \frac{1}{4}I+ \frac{1}{2}I= (A+ \frac{1}{2}I)^2+ (B+ \frac{1}{2}I)^2+ \frac{1}{2}I$ Tags det, matrix, pls, problem, probleme, solve Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ziradus50 Linear Algebra 3 September 22nd, 2013 12:30 AM leo75 Algebra 1 June 27th, 2013 08:12 AM Norm850 Linear Algebra 3 February 29th, 2012 02:45 PM jonbryan80 Linear Algebra 1 August 9th, 2010 01:21 AM RMG46 Linear Algebra 2 July 5th, 2010 11:24 PM

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