
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 26th, 2014, 08:29 PM  #1 
Newbie Joined: Dec 2014 From: Romania Posts: 5 Thanks: 0 Math Focus: linear algebra  what a way to solve the determinant of this kind of a matrix?
i tried raw operations. but not that confident about it. someone can show me some guidness please? 8x48 x+24 x+24 x+24 x+24 x+24 8x48 x+24 x+24 x+24 x+24 x+24 8x48 x+24 x+24 x+24 x+24 x+24 8x48 x+24 x+24 x+24 x+24 x+24 8x48 Last edited by greg1313; December 27th, 2014 at 06:54 AM. 
December 28th, 2014, 01:54 AM  #2 
Newbie Joined: Dec 2014 From: Romania Posts: 5 Thanks: 0 Math Focus: linear algebra 
i already solved it . but no one can give a second idea ? i just added the columns and took 4x+48 as a common facor 
January 9th, 2015, 05:31 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
There is no matrix given. What matrix are you referring to?

January 9th, 2015, 06:24 AM  #4 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
I presume he means $\displaystyle A = \left[\begin{array}{ccccc} 8x48 & x+24 & x+24 & x+24 & x+24 \\ x+24 & 8x48 & x+24 & x+24 & x+24 \\ x+24 & x+24 & 8x48 & x+24 & x+24 \\ x+24 & x+24 & x+24 & 8x48 & x+24 \\ x+24 & x+24 & x+24 & x+24 & 8x48 \\ \end{array}\right]$ You can simplify it a little bit using a scalar operation before attempting to find the determinant: $\displaystyle A = (x+24)\left[\begin{array}{ccccc} 8\left(\frac{x+6}{x+24}\right) & 1 & 1 & 1 & 1 \\ 1 & 8\left(\frac{x+6}{x+24}\right) & 1 & 1 & 1 \\ 1 & 1 & 8\left(\frac{x+6}{x+24}\right) & 1 & 1 \\ 1 & 1 & 1 & 8\left(\frac{x+6}{x+24}\right) & 1 \\ 1 & 1 & 1 & 1 & 8\left(\frac{x+6}{x+24}\right) \\ \end{array}\right]$ Because $\displaystyle det(kA) = k^ndet(A)$, where k is a scalar multiple and n is the rank of the square matrix, $\displaystyle det(A) = (x+24)^5\left\begin{array}{ccccc} 8\left(\frac{x+6}{x+24}\right) & 1 & 1 & 1 & 1 \\ 1 & 8\left(\frac{x+6}{x+24}\right) & 1 & 1 & 1 \\ 1 & 1 & 8\left(\frac{x+6}{x+24}\right) & 1 & 1 \\ 1 & 1 & 1 & 8\left(\frac{x+6}{x+24}\right) & 1 \\ 1 & 1 & 1 & 1 & 8\left(\frac{x+6}{x+24}\right) \\ \end{array}\right$ Maybe this one will be easier to manage! 

Tags 
determinant, kind, matrix, solve, yhe 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Determinant 4x4 matrix  jones123  Linear Algebra  3  April 24th, 2013 03:16 AM 
matrix and determinant  helloprajna  Linear Algebra  2  December 8th, 2012 06:31 AM 
determinant of a matrix  bullroarer  Algebra  2  May 23rd, 2009 02:44 PM 
Determinant Matrix 7x7  battery  Linear Algebra  1  November 21st, 2008 11:45 AM 
Determinant 4x4 matrix  jones123  Calculus  1  December 31st, 1969 04:00 PM 