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how do i solve simultaneous equations using matrices

Guest May 29, 2017
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 #1
avatar+76929 
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Give me the equations and I'll show you......equations in two variables are a little easier than with larger systems......

 

 

cool cool cool

CPhill  May 29, 2017
 #2
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4x-5e=18

3e+5x=4

Guest May 29, 2017
 #3
avatar+76929 
+1

 

4x-5e=18

3e+5x=4

 

Rearrange as

 

4x - 5e  =  18

5x + 3e  = 4              assuming "e"  is a variable, we have the matrix , A =

 

[ 4   - 5  

[ 5    3 ]   we need to find the inverse  of this matrix

 

We have the form

 

[ a  b

 c  d ]       the inverse is given by

 

 

1 /  [ ad  - bc ]   [ d   -b               =

                           -c  a ]   

 

1 /  [ 4*3 - (-5)*(5) ]   [  3    5         =

                                    -5   4 ] 

 

1 /  [ 12 + 25]   [    3    5           =

                            -5    4 ]

 

1/[37]  [  3   5        =

             -5   4 ]

 

            [  3/37     5/37

              -5/37     4/7]

 

Call this  matrix the inverse of A  = A-1 

And  call  the  column  matrix   [ 18           =   b

                                                     4]

 

And  the solution for  ( x, e)   is given by

 

A-1  *  b    =    [ 3/37   5/37   *      [18      =

                        -5/37   4/37 ]            4]

 

 ( (3/37)*18 +  (5/37)* 4,  (-5/37)*(18) + (4/37)*(4)   ) 

 

(    74/ 37, -74/ 37 )   =

 

(2, -2 )   =  (x, e)

 

Obviously, this is more easily solved with either substitution, elimination [or with Cramer's Rule]

 

 

 

cool cool cool

CPhill  May 29, 2017

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