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Math Help - I need major help :(

  1. #1
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    I need major help :(

    Questions can be found here:
    http://www.freewebs.com/kgpretty/math.JPG


    I attempted #4.. can you use 4 .. determinants? to solve the equation like:
    Code:
    x|k  l|  -a|l  m|   x|k  l|   -a|l  m|
     |m  n|    |n  o|    |o  k|     |n  o|
    For #7, I've think I've got that covered. Just tell me.. would the augmented matrix be:
    |log1 log1 log1|0|
    to represent the first row?

    or |1 1 1|0|, where log is factorised out?


    For all the other questions.. I simply don't know what to do
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  2. #2
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    Quote Originally Posted by kgpretty View Post


    I attempted #4..
    No only 3.
    Expand along the first row:
    Code:
    x [x b]-a[a b]+b[a x]
       [b x]   [a x]    [a b]   =0
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  3. #3
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    For your other problem.
    Do my excersice.
    Show that the determinant below is always zero.
    ----
    Once you have done that you can use the fact, x,y,z>0
    log(2x)=log2 +log x
    log(2y)=log2 +log y
    log(2z)=log2 +log z
    log(3x)=log3+log x
    log(3y)=log3+log y
    log(3z)=log3+log z
    Let,
    a=log x
    b=log y
    c=log z
    Then you end with,
    Code:
    a                b            c
    a+log 2  b+log 2  c+log 2
    a+log 3  b+log 3  c+log 3
    Then use that result.
    Attached Thumbnails Attached Thumbnails I need major help :(-picture8.gif  
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  4. #4
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    Quote Originally Posted by ThePerfectHacker View Post
    No only 3.
    Expand along the first row:
    Code:
    x [x b]-a[a b]+b[a x]
       [b x]   [a x]    [a b]   =0
    When I expand along the first row, the result isn't equal to 1.
    From the first expansion, you get:
    x^3 - b^2x

    There's no x^3 in the other expansions to cancel the x^3 already there. How can I be equal to 0?
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  5. #5
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    Quote Originally Posted by kgpretty View Post
    When I expand along the first row, the result isn't equal to 1.
    From the first expansion, you get:
    x^3 - b^2x

    There's no x^3 in the other expansions to cancel the x^3 already there. How can I be equal to 0?
    Expand it each determinant.
    x(x^2-b^2)-a(ax-ab)+b(ab-ax)=0
    Thus,
    x^3-xb^2-a^2x+a^2b+ab^2-abx=0
    Thus,
    x^3-x(b^2-ab+a^2)+a^2b+ab^2=0
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  6. #6
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    Quote Originally Posted by ThePerfectHacker View Post
    Expand it each determinant.
    x(x^2-b^2)-a(ax-ab)+b(ab-ax)=0
    Thus,
    x^3-xb^2-a^2x+a^2b+ab^2-abx=0
    Thus,
    x^3-x(b^2-ab+a^2)+a^2b+ab^2=0
    I'm sorry, I don't get it.
    How does x^3-x(b^2-ab+a^2)+a^2b+ab^2 equal to 0?
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  7. #7
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    Quote Originally Posted by kgpretty View Post
    I'm sorry, I don't get it.
    How does x^3-x(b^2-ab+a^2)+a^2b+ab^2 equal to 0?
    Because the left hand side (determiant) was expaned into this equation. Now the problem says to solve when it is equal to zero.
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