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December 13th, 2014, 09:27 PM   #1
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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.
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December 14th, 2014, 08:51 AM   #2
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You don't, as a 3 by 2 matrix isn't a square matrix.
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December 15th, 2014, 06:00 AM   #3
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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
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December 15th, 2014, 06:09 AM   #4
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A is a 2*2 matrix. Assign a letter to each of the four elements, multiply and see whether it has a solution.
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December 16th, 2014, 12:31 AM   #5
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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
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December 16th, 2014, 04:26 AM   #6
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: 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
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December 16th, 2014, 04:50 AM   #7
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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.
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December 16th, 2014, 05:07 AM   #8
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@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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