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Math Help - Augmented matrix

  1. #1
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    Augmented matrix

    Posted: Mon, 18 Sep 2006 21:37:07 GMT Post subject: rref augmented matrix (already reduced)


    i am given the already reduced matrix of : 1 2 0 3
    0 0 1 5
    0 0 0 0

    i know that the linear system is x1= -3 and x2= 5 and x3= 0 but i need to find how to write the infinite solution of the system using variable t.

    All I can come up with is: 1x sub 1 - 2x subs = -3
    1x sub 3 = 5
    x sub 3 = x sub 3

    It doesnt make sense to me when I think I need to let X sub 3 = t

    How can i get an infinite solution using the variable t for this system?
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  2. #2
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    [size=3]Hello, dekorn24!


    i am given the already reduced matrix:
    . . 1 2 0 | 3
    . . 0 0 1 | 5
    . . 0 0 0 | 0

    I need to find how to write the infinite solution of the system using variable t.

    We have: .x + y .= .3
    . . . . . . . . . . .z .= .5

    Get everthing "in terms of y"
    . . . . . . . . . x .= .3 - y
    . . . . . . . . . y .= .y
    . . . . . . . . . z .= .5

    On the right, replace y with t.

    And we have: .x .= .3 - t
    . . . . . . . . . . .y .= .t
    . . . . . . . . . . .z .= .5

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