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Math Help - find x

  1. #1
    Senior Member DivideBy0's Avatar
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    find x

    A = [4 3]
    ......[2 1]

    If AX = [3 4]
    ..........[1 6]

    Find X.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by DivideBy0 View Post
    A = [4 3]
    ......[2 1]

    If AX = [3 4]
    ..........[1 6]

    Find X.
    Use Gaussian ellimination on the augmented matrix:

    Code:
     
    [4 3 | 3 4]
    [2 1 | 1 6]
     
    [0 1 | 1 -8]
    [2 1 | 1  6]
     
    [0 1 | 1 -8]
    [2 0 | 0 14]
     
    [1 0 | 0  7]
    [0 1 | 1 -8]
     
    Now  check:
     
    [4 3][0  7]  =  [3 4]
    [2 1][1 -8]     [1 6]
    RonL
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  3. #3
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    Hello, DivideBy0!

    Here's a primitive way to solve it . . .


    A = [4 3]
    . . . [2 1]

    If AX = [3 4]
    . . . . . .[1 6]

    Find X.
    Let X .= .| a b |
    . . . - . . .| c d |


    Then we have: . | 4 3 | . | a b | -= -| 3 4 |
    . . . . . . . . . . . .| 2 1 | . | c d | . . . | 1 6 |


    Hence: . | 4a + 3c . 4b + 3d | -= -| 3 4 |
    . . - . - . | 2a + .c . .2b + -d | . . . | 1 6 |


    And we have two system of equations:

    . . 4a + 3c .= .3 . . . . 4b + 3d .= .4
    . . 2a + .c -= -1 . . . . 2b + . d .= .6


    Solve by your favorite method and get:

    . . a = 0, .b = 7, .c = 1, .d = -8

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  4. #4
    Junior Member Singular's Avatar
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    A = [4 3]
    . . . [2 1]

    AX = [3 4]
    . . . .[1 6]

    A'AX = A' [3 4]
    . . . . . . [1 6]
    .....X.= [1 -3][3 4]
    . . . . . [-2 4][1 6]

    A'=A inverse

    if A=[a b]
    .....[c d]

    A'=[d -b]
    .....[-c a]
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  5. #5
    Super Member

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    Hello, singular!

    You left out the fraction . . .


    . . . . . . | a b |
    Given: . | . - .|
    . . . . . . | c d |


    . . . . - . . . . . . .| . . d . . . . .-b . - |
    . . . . - . . . . . . .| -------- . --------- |
    . . . . - . . . . . . .| ad - bc . ad - bc .|
    The inverse is: . | . . . . . . . . . . . . |
    . . . . - . . . . . . .|. . -c . . . . . a . . .|
    . . . . - . . . . . . .| -------- . --------- |
    . . . . - . . . . . . .| ad - bc . ad - bc .|


    In baby-talk:
    . . Switch the elements on the main (southeast) diagonal.
    . . Change the signs of the elements on the other diagonal.
    . . Divide all elements by the determinant of the matrix.

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  6. #6
    Junior Member Singular's Avatar
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    Quote Originally Posted by Soroban View Post
    [size=3]Hello, singular!

    You left out the fraction . . .
    i'm so stupid......sorry...
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