
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 24th, 2019, 04:51 AM  #1 
Newbie Joined: Jun 2019 From: London Posts: 13 Thanks: 0  Calculate a determinant
How could i calculate determinant this matrix. if it doesn't have exact dimension

July 24th, 2019, 06:00 AM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 213 Thanks: 90  The central diagonal {(i,i)} has the product $\displaystyle (a+b)^N$. This is a "positive" diagonal. For a 3x3 or higher, all other diagonals have at least one zero in them. (Note, the "1"s diagonal has the zero from (1,N) and the "ab"s diagonal has the zero from (N,1). All the downandtotheleft diagonals also have at least one zero.) The determinant should be $\displaystyle (a+b)^N \forall N \geq 3$, where N is the size of the matrix. Try it for 3x3 and 4x4 to test it. Happens to work for 1x1, also. 2x2 would be a special case.

July 24th, 2019, 07:47 AM  #3 
Senior Member Joined: Jun 2019 From: USA Posts: 213 Thanks: 90 
Scratch the above answer. It's wrong, and for some reason I can't edit it. Solved it by example (up to 5x5): $\displaystyle 2 \times 2 = a^2 + ab + b^2$ $\displaystyle 3 \times 3 = a^3 + a^2b + ab^2 + b^3$ $\displaystyle N \times N = \sum_{i=0}^{N} a^ib^{Ni}$ Last edited by DarnItJimImAnEngineer; July 24th, 2019 at 08:13 AM. 

Tags 
calculate, determinant 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculate the determinant of the matrix  mathodman25  Linear Algebra  0  June 17th, 2019 03:09 PM 
Best way to calculate a 5x5 determinant?  coltson  Linear Algebra  10  January 9th, 2018 10:03 AM 
Calculate determinant  iranch  Algebra  2  November 29th, 2015 01:44 PM 
determinant  robertson  Linear Algebra  8  October 25th, 2014 10:05 PM 
determinant  afrim  Linear Algebra  1  October 10th, 2011 10:50 AM 