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Math Help - linear combination urgent help

  1. #1
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    linear combination urgent help

    Let A= . -1 1 -1 3
    3 1 -1 -1
    2 -1 -2 1
    a) Find a matrix B that is row equivalent to A.
    b) Determine whether the fourth column vector forms a linear combination with the first three column vectors.
    c) Show that the first three column vectors are linearly independent. Explain.

    i need help to practice this i have test day after tommorow..i need hard pracrice///
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  2. #2
    Super Member Aryth's Avatar
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    Re: linear combination urgent help

    For a), just do any of the row operations and that matrix will be row equivalent to A.

    For b), Just set the equation up, a[-1 \ 3 \ 2]^T + b[1 \ 1 \ -1]^T + c[-1 \ -1 \ -2]^T = [3 \ -1 \ 1]^T

    Where T refers to the transpose. solve for a, b, and c. You could even use a few guesses to see what you get, if you wanted.

    For c), You need to show that the first three column vectors satisfy this property:

    A set of vectors, v_1,v_2,v_3,\cdots,v_n are linearly independent if and only if a_1v_1 + a_2v_2 + a_3v_3 + \cdots + a_nv_n = 0 implies that a_1 = a_2 = a_3 = \cdots = a_n = 0.
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  3. #3
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    Re: linear combination urgent help

    i was having much problem in b now i just finished doing this.thankyou so much.may god bless u.
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