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# simultaneous matrices

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how do i solve simultaneous equations using matrices

Guest May 29, 2017
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#1
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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......

CPhill  May 29, 2017
#2
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4x-5e=18

3e+5x=4

Guest May 29, 2017
#3
+76925
+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]

CPhill  May 29, 2017

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