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Math Help - Matrix Algebra.

  1. #1
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    Cool Matrix Algebra.

    Hey everyone,

    Could someone please shine some light on this question, I'm not sure I fully understand how it's worded?

    Chris.



    A range of metallic alloys are tested for electrical conductivity and give the following results for identically sized samples.

    25% copper with 75% tin gave a reading of 0.0071 Ohms
    65% copper with 35% cadmium gave a reading of 0.0049 Ohms
    40% copper with 40% tin and 20% cadmium gave a reading of 0.0060 Ohms

    Using matrix algebra, determine the resistance of an equally sized sample for each of the pure metals

    (a) Copper
    (b) Tin
    (c) Cadmium
    Last edited by mr fantastic; June 2nd 2011 at 07:20 PM. Reason: Title.
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  2. #2
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    Quote Originally Posted by ckeller View Post
    Hey everyone,

    Could someone please shine some light on this question, I'm not sure I fully understand how it's worded?

    Chris.



    A range of metallic alloys are tested for electrical conductivity and give the following results for identically sized samples.

    25% copper with 75% tin gave a reading of 0.0071 Ohms
    65% copper with 35% cadmium gave a reading of 0.0049 Ohms
    40% copper with 40% tin and 20% cadmium gave a reading of 0.0060 Ohms

    Using matrix algebra, determine the resistance of an equally sized sample for each of the pure metals

    (a) Copper
    (b) Tin
    (c) Cadmium
    let [A] be a 3x3 matrix with percentages of copper, tin, and cadmium for each alloy

    let [B] be a 3x1 matrix of the unknown resistances of each individual metal

    let [C] be a 3x1 matrix of the measured resistance of each alloy

    [A][B] = [C]

    solve for matrix [B]

    My calculator sez the resistances for copper, tin, and cadmium to be .0056, .0076, and .0036 ohms respectively.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    let [A] be a 3x3 matrix with percentages of copper, tin, and cadmium for each alloy

    let [B] be a 3x1 matrix of the unknown resistances of each individual metal

    let [C] be a 3x1 matrix of the measured resistance of each alloy

    [A][B] = [C]

    solve for matrix [B]

    My calculator sez the resistances for copper, tin, and cadmium to be .0056, .0076, and .0036 ohms respectively.
    Hey Thanks very much for your reply it makes sense now.. although I have derived the same but smaller... 0.000056, 0.000076, and 0.000036...

    I wonder where I went wrong there
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  4. #4
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    Quote Originally Posted by ckeller View Post
    Hey Thanks very much for your reply it makes sense now.. although I have derived the same but smaller... 0.000056, 0.000076, and 0.000036...

    I wonder where I went wrong there
    I suspect you failed to represent the given percentages as their decimal equivalents.
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  5. #5
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    Quote Originally Posted by skeeter View Post
    I suspect you failed to represent the given percentages as their decimal equivalents.
    Hey yeah I realized that just as I posted my last comment, silly me lol

    Thanks for your help.
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