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Math Help - Help needed in matrices and solutions?

  1. #1
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    Help needed in matrices and solutions?

    The augmented matrices of three systems of linear equation are given in row echelon form below.

    (i)
    |1 0 2 1|
    |0 0 1 2|
    |0 0 0 1|

    (ii)
    |1 0 2 1|
    |0 1 −1 2|
    |0 0 1 1|

    (iii)
    |1 0 2 1|
    |0 0 1 2|
    |0 0 0 0|

    One of the systems has no solutions, one has one solution, and one has an infinite number of solutions. Identify which is which and solve the two that have solutions.


    *give ur workings and a clear answer.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by federer View Post
    The augmented matrices of three systems of linear equation are given in row echelon form below.

    (i)
    |1 0 2 1|
    |0 0 1 2|
    |0 0 0 1|

    (ii)
    |1 0 2 1|
    |0 1 −1 2|
    |0 0 1 1|

    (iii)
    |1 0 2 1|
    |0 0 1 2|
    |0 0 0 0|

    One of the systems has no solutions, one has one solution, and one has an infinite number of solutions. Identify which is which and solve the two that have solutions.


    *give ur workings and a clear answer.
    Well the first has no solutions as the last row corresponds to an equation:

    0 \times x+0 \times y + 0 \times z=1

    Which has no solutions.

    The last one has an ifinite number of solutions as there are only two effective equations, and they are linearly independednt.

    The middle one has a unique solution and you show that by solving the system.

    RonL
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