Maths ගානක්.

VPS09

Well-known member
  • Sep 13, 2014
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    maharagama
    මේක සොල්ව් කරල දියල්ලකො දන්න කෙනෙක්. :sorry:
    මොරටු BIT පාස්ට් පෙපර් ගානක් බන්.

    9827f16c-2dd5-40b1-52e0-2ea99bda6a96.png


    බම්පියක් දාල හෙල්ප් එකක් දෙන්න මචන් දන්න කෙනෙක් දකිනකම්. :love::love:
     

    suicxde

    Well-known member
  • Jun 14, 2017
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    6ftunder
    adoo godaa. meken theruna hadana hati.
    antima eka hadana hati danno nm me wage hadala dapanko.

    mata neme bn kellata kiyala denna :love:




    Eka danne na bn.man A/L mathaka widihata oya kare.net eken baluwama hari.

    Anik eka dakketh ada bn :(
     

    VPS09

    Well-known member
  • Sep 13, 2014
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    maharagama
    me krame da use karanna one 1st 2nd ewa hadanna.


    Solve for x, y and z in the system of equations below
    a8731da3-c004-4767-a6f2-a9ab2015cad1.gif
    Solution:
    The first step is to turn three variable system of equations into a 3x4 Augmented matrix.
    c0b75f91-0812-482b-8dc6-71841bfa74f4.gif
    Next we label the rows of the matrix:
    cd917ddd-6a0b-4037-9efa-053ff059c332.gif
    Since in the above augmented matrix we can't find any rows with one as the leading coefficient, we don't need to perform a row switching operation. However, we do need to modify row 1 such that its leading coefficient is 1.
    We can achieve this by multiplying row 1 by 1⁄3:
    c27db68b-be23-4e21-bd1e-65031a1e070e.gif
    Next we need to change all the entries below the leading coefficient of the first row to zeros.
    For the second row, we can achieve this by first multiplying through by-1⁄3 and then adding the result to row 1.
    9ae6eecc-4fc8-4e87-be0b-6783e0594793.gif
    Adding the result to row 1:
    757e11bd-c818-4963-8c35-91951e9a8ffe.gif
    We then move on to row 3; here we multiply the row by -1⁄5 and then add the result to row 1 in order to zero out the first element.
    312ece20-78f1-4422-9953-a4cc97e33bd4.gif
    Adding the result to row 1:
    e7938e76-cd10-40d4-ac88-ddccdfe60526.gif
    We need the leading element in the second row to also be one. We obtain this result by multiplying the second row by -3⁄2:
    9e6fc7f5-6278-4805-8712-c9106924afc7.gif
    Next we zero out the element in row three beneath the leading coefficient in row two. To achieve this, we multiply the third row by5⁄4
    cf7539e4-20b8-4638-9075-758a8f52dffb.gif
    Adding the result to row 2:
    1c709a2d-95e2-4d5f-90ea-1692202b913d.gif
    Finally we multiply row 3 by -12 in order to have the leading element of the third row as one:
    f48c15b2-1473-48ca-96f1-7f0e94f21cda.gif
    From the above matrix, we solve for the variables starting with z in the last row
    9f06d33f-46eb-454b-978c-7a819499a7fd.gif
    Next we solve for y by substituting for z in the equation formed by the second row:
    1aea0c0b-f635-4b88-82f0-a9be9520e4b3.gif

    927218b9-9587-4b7c-91b3-c6284d485cc2.gif

    abefe3bf-1fdc-41d3-be84-d275e8db71d8.gif
    Finally we solve for x by substituting the values of y and z in the equation formed by the first row:
    6cc321e6-ed72-4598-ab11-b1d81a6103f1.gif

    cfa28acb-28c1-431b-a1de-ccb59a3c6ac9.gif

    6c967896-9fbc-4fbf-8ecb-6dc148019a0d.gif
    Therefore, the solution to the system of equations is {x,y,z} = {1,-2,1}
     

    suicxde

    Well-known member
  • Jun 14, 2017
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    oke b kaalla hadanna bane bn
    math error ekak enawa

    ekko eka matrix wala wena mokakhari scene ekakin hadanne.naththan gaana waradi

    samagami thuna wisadanna ba 2nd eke


    1st eka haduweth me method ekatamai


    YYq9uUM.jpg
     
    Last edited:

    Vandetta

    Well-known member
  • Dec 29, 2015
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    V
    there are 3 methods to solve it
    google : 1 inverse matrix method
    2 cramers rule
    3 Gaussian elimination (with row echelon form)
     

    peter001

    Well-known member
  • Nov 1, 2012
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    Colombo
    Matricex system ekak solve karanna widi 3k thiyenawa,

    1. Gaussian elimination
    2. Cramer's rule
    3. Inverse matrix method
    Cramer's rule eka lesi habai hama welwakama eka karannath ba, matrix ekaka determiantion eka 0 unoth ba nattan eka use karapn eka lesi elimination and inverse ekata wada
     
    Last edited:

    VPS09

    Well-known member
  • Sep 13, 2014
    6,727
    2,138
    113
    maharagama
    oke b kaalla hadanna bane bn
    math error ekak enawa

    ekko eka matrix wala wena mokakhari scene ekakin hadanne.naththan gaana waradi

    samagami thuna wisadanna ba 2nd eke


    1st eka haduweth me method ekatamai


    YYq9uUM.jpg

    Ado uba initial Matrix ekata dala cal eke gahala da bn Uttare ganne. Matrix 5k 6k pahalata hadan yana wenawa neda manual karanawa nm.