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December 13th, 2014, 09:27 PM  #1 
Newbie Joined: Dec 2014 From: pakistan Posts: 15 Thanks: 0  How to find inverse of 3 by 2 matrix dont use echelon form
hi, how to find inverse of 3 by 2 matrix.dont use echelon form,reduced echelon form.use cofactors method. 
December 14th, 2014, 08:51 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361 
You don't, as a 3 by 2 matrix isn't a square matrix.

December 15th, 2014, 06:00 AM  #3 
Newbie Joined: Dec 2014 From: pakistan Posts: 15 Thanks: 0  How to find inverse of 3 by 2 matrix dont use echelon form
to see the real question plz click link below https://www.dropbox.com/s/ug9e2n702j...atrix.bmp?dl=0 in this question find value of matrix A. Last edited by ormara; December 15th, 2014 at 06:03 AM. Reason: revised post 
December 15th, 2014, 06:09 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361 
A is a 2*2 matrix. Assign a letter to each of the four elements, multiply and see whether it has a solution.

December 16th, 2014, 12:31 AM  #5 
Newbie Joined: Dec 2014 From: pakistan Posts: 15 Thanks: 0  How to find inverse of 3 by 2 matrix dont use echelon form
did exactly the same but the book's answer was different than mine.how can you say A is a 2 by 2 matrix.it can be 3 by 3,1 by 3,3 by 4,3 by 2 etc. (off topic)why my thread was moved. Last edited by ormara; December 16th, 2014 at 12:39 AM. Reason: adding more comments 
December 16th, 2014, 04:26 AM  #6 
Newbie Joined: Dec 2014 From: pakistan Posts: 15 Thanks: 0  : How to find inverse of 3 by 2 matrix dont use echelon form
[SOLVED] .i yesterday solved this problem by the method that you described.but answer was wrong.but now about 25 minutes ago i solved it by same method and now answer is Right.BUT if we look at the question in the link again.order of first matrix is 3 by 2 and order of A is unknown and order of the right hand side matrix is 3 by 2.according to formula order of A x B = C. m by n ,n by p then order of C is m by p.but the answer is correct in book but its order according to order formula is 3 by 2 but answer is 2 by 2. Why? can you or any one else find answer.click link below to see its answer. https://www.dropbox.com/s/zzf40eqv1h...nswer.bmp?dl=0 Answer has order 2 by 2. Last edited by ormara; December 16th, 2014 at 05:03 AM. Reason: adding new contents 
December 16th, 2014, 04:50 AM  #7 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,161 Thanks: 734 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
$\displaystyle A$ must be a 2 x 2 matrix because if it didn't the matrix on the righthand side would have different dimensions. $\displaystyle \left[\begin{array}[cc] \\ 5 & 1 \\ 0 & 0 \\ 3 & 1 \\ \end{array}\right] \left[\begin{array}[cc] \\ A_{11} & A_{12} \\ A_{21} & A_{22} \\ \end{array}\right] = \left[\begin{array}[cc] \\ 3 & 7 \\ 0 & 0 \\ 7 & 2 \\ \end{array}\right]$ As Hoempa suggested, we multiply out the matrices to get the following simultaneous equations: $\displaystyle 5A_{11}  A_{21} = 3$ $\displaystyle 5A_{12}  A_{22} = 7$ $\displaystyle 3A_{11} + A_{21} = 7$ $\displaystyle 3A_{12} + A_{22} = 2$ The solutions to these are $\displaystyle A_{11} = \frac{5}{4}$ $\displaystyle A_{12} = \frac{5}{8}$ $\displaystyle A_{21} = \frac{13}{4}$ $\displaystyle A_{22} = \frac{31}{8}$ So $\displaystyle A = \left[\begin{array}[cc] \\ A_{11} & A_{12} \\ A_{21} & A_{22} \\ \end{array}\right] = \frac{1}{8} \left[\begin{array}[cc] \\ 10 & 5 \\ 28 & 31 \\ \end{array}\right]$ Last edited by Benit13; December 16th, 2014 at 04:53 AM. 
December 16th, 2014, 05:07 AM  #8 
Newbie Joined: Dec 2014 From: pakistan Posts: 15 Thanks: 0 
@Benit13 order formula is if we have a matrix equation A x B = C A has order m by n, B has order n by p, then its product A x B has order m by p.This formula is in textbooks.so by this formula answer should have order 3 by 2 but answer has order 2 by 2. 

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