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Math Help - Two Liner Algebra Problems

  1. #1
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    Exclamation Two Liner Algebra Problems

    Hello

    1.-Could you please help me to find all solutions to the following system of equations.

    (1-i)x-iy=0
    2x+(1-i)y=0



    2.-Prove that the interchange of two rows of a matrix can be accomplished by a finite sequence of elementary row operations of the other two types.

    Thanks a lot
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    1. Note that 2=(1+i)(1-i)=-i(1+i)^2.

    2. Suppose you want to interchange R_1=x and R_2=y.

    First add R_2 to R_1 to get R_1=x+y.

    Next subtract R_1 from R_2 to get R_1=x+y, R_2=-x.

    Next add R_2 to R_1 to get R_1=y, R_2=-x. Finally multiply R_2 by -1 (interchanging two rows or columns changes the sign of the determinant).
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