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November 9th, 2018, 08:16 PM  #1 
Banned Camp Joined: Nov 2018 From: Mumbai Posts: 32 Thanks: 1  Inverse of a matrix of decimal or floating numbers.
Can we find the Inverse of a 3*3 matrix having the following decimal number elements? 1.2 2.3 4.5 6.1 4.2 2.9 7.4 3.5 8.7 Thanks & Regards, Prashant S Akerkar 
November 9th, 2018, 08:23 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,424 Thanks: 759  
November 9th, 2018, 09:35 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 21,105 Thanks: 2324 
$\begin{pmatrix} 2639/8482 & 426/8482 & 1223/8482 \\ 3161/8482 & 2286/8482 & 2397/8482 \\ 973/8482 & 1282/8482 & 899/8482 \end{pmatrix}$ 
November 9th, 2018, 10:00 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,340 Thanks: 983 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
November 10th, 2018, 02:08 AM  #5 
Banned Camp Joined: Nov 2018 From: Mumbai Posts: 32 Thanks: 1 
Thanks. Can it become complex to compute the Inverse if the precision is increased for the decimal numbers in the Matrix? Example: 34.333333333 51.222222785 98.333556677 12.555555555 76.444555532 65.234567879 34.888855338 68.542666669 54.236666856 Thanks & Regards, Prashant S Akerkar 
November 10th, 2018, 02:04 PM  #6  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,340 Thanks: 983 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
November 10th, 2018, 03:00 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 21,105 Thanks: 2324 
If the numbers in the matrix are known to be approximate, you have a difficulty if the determinant of the matrix seems to be zero (or very close to zero).

November 10th, 2018, 03:16 PM  #8 
Senior Member Joined: Oct 2009 Posts: 905 Thanks: 354  Very common misunderstanding! It is not a problem if the determinant is close to 0. It is the condition number that matters, not the determinant. Contrary to expectation, a small determinant does not indicate nearinvertibility, nor it is a problem.

November 11th, 2018, 02:39 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 21,105 Thanks: 2324 
$\begin{pmatrix} 34.333333333 & 51.222222222 & 98.333333333 \\ 12.555555555 & 76.444444444 & 65.222222222 \\ 21.777777778 & 25.222222222 & 33.111111111 \end{pmatrix}$ The above matrix, where the first two rows are similar to the corresponding rows in the matrix supplied by akerkarprash, but the third row is the difference of the first two rows, so that the determinant of the matrix is zero, doesn't have an inverse. Nevertheless, the website mentioned above calculates an inverse for it (as does wolframalpha). Of course the condition number is infinite in this case. If I change the final decimal place of one of the entries in this matrix, the determinant of the matrix is very small and the above website calculates its inverse inaccurately, but the condition number is large. For a matrix of this type, you are effectively asserting that its determinant can be very close to zero without its condition number being very large. Can you give an example of this? 

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