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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 right-hand 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. Tags echelon, find, form, inverse, matrix 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 artiny Linear Algebra 2 October 18th, 2013 10:02 AM shine123 Linear Algebra 8 August 31st, 2012 10:05 AM questioner1 Linear Algebra 3 August 16th, 2012 08:03 AM mps727 Algebra 4 June 20th, 2010 08:40 AM yyttr4 Linear Algebra 0 June 3rd, 2010 03:41 PM

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