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math

posted by on .

Using the inverse of:
2 1
-3 4
Find
2x+y=2
-3x+4y=1

  • math - ,

    It is supposed to be a matrix.
    2, 1
    -3, 4
    but i donot know how to put the brackets. i used commas to separate the numbers

  • math - ,

    well, I will use gauss jordan, see the link I gave you.
    2,1,1,0
    -3,4,0,1

    +1, .5 , .5, 0
    -3, 4. , 0 , 1
    multiply top by +3 and add to bottom
    +1, .5 , .5 , 0
    0 , 5.5, 1.5, 1
    divide second row by 5.5
    +1, .5 , .5 , 0
    0 ,1.0, .273,.182
    subtract half the second row from the first to get a new first
    +1 , 0 , .364, -.091
    0 , 1.0, .273, .182
    so I think the inverse is
    .364 , -.091
    .273 , .182
    multiply that by
    2
    1
    and get
    x = 2*.364 - 1* .091 = .637
    y = 2*.273 +1 * .182 = .728
    check
    2*.637 + .728 = close enough to 2
    -3*.637 + 4*.728 = close enough to 1

  • Took me a while - ,

    I have not inverted a matrix by hand for a while :)

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