product matrix

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which product represents the solution to the system 3x+4y=-2 and 2x+5y=6

[3 2]*[-2
[4 5] [6]

1/7[3 2]*[-2]
[4 5] [6]

[5 -2]*[-2]
[-4 3] [6]

1/7[5 -4]*[-2]
[-2 3] [6]

could someone explain

  • product matrix -

    your given system can be written in the following matrix form
    [ 5-4]*[x]=[-2]
    [-2 3] [y] [6]

    the inverse of the first matrix is
    1/17 of
    [ 5-4]
    [-2 3]

    if you multiply the left side by that inverse you get the identity matrix
    [1 0]
    [0 1]

    of course you would then also multiply the right side by that , so it looks like the last answer is the correct one

  • product matrix (getting careless) -

    oops!!
    that first matrix of course should have been

    [ 3 4]*[x]=[-2]
    [ 2 5] [y] [6]

    I copied incorrectly from my paper

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