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Math Help - linear combinations

  1. #1
    DrZ
    DrZ is offline
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    linear combinations

    let

    A=
    1 2
    1-2

    b=
    4
    0

    c=
    -3
    -2

    a) write b as a linear combination of the column vectors a1 and a2
    b) use the result from a to determine solution of linear system Ax = b. does the system have any other solutions? explain.
    c) write c as a linear combination of a1 and a2.


    I got part a) I think

    b = 2a1 +a2 since 2 times a1 plus one a2 equals the b matrix.

    so then part b)

    x would be

    2
    1
    since

    2 times A is b
    1

    c) is where I am stuck

    I cant figure out a combination for
    c=
    -3
    -2

    I feel I need to subtract a2 from a1, but then the bottom position wont be -2 if I subtract a1 by 2a2
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  2. #2
    MHF Contributor

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    Tejas
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    666
    solve the two equations:

    x-2y = -2
    x+2y = -3

    then x will be what you multiply a1 by, and y will be what you multiply a2 by.

    hint: they won't be integers.
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  3. #3
    DrZ
    DrZ is offline
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    Thanks. The TA for our class explained it the same way.

    made a matrix and reduced it and got the solution.
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