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Sum of Products Help

  1. Sep 3, 2009 #1
    I don't quite understand the method to solve this type of question.

    Let x=(-3,2,5), y=(2,4,-5), and z=(1,6,7). Calculate:
     

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  2. jcsd
  3. Sep 3, 2009 #2
    I view such qns playing with 'arrays' and 'susbstituion'.

    Generally, i will view it this way:-

    x is an array of (-3,2,5)
    y is an array of (2,4,-5)

    first part is u do the summation first - i call it inner.

    Inner: (-3)(2) + (2)(4)

    Then you do the Products - i call it outer.

    But is your question complete? Theres no 'j' in your formulaes pasted.
     
  4. Sep 3, 2009 #3

    HallsofIvy

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    What you have written,
    [tex]\prod_{j= 1}^3\sum_{i=1}^2 x_iy_i[/tex] and
    [tex]\sum_{j=1}^3\prod_{i=1}^2 x_iy_i[/tex]
    are just
    [tex]\prod_{j=1}^3(x_1y_1+ x_2y_2+ x_3y_3)= \prod_{j=1}^3((-3)(2)+ (2)(4)+ (5)(-5))= \prod_{j=1}^3(-6+ 8- 10)= 3(8)= 24[/tex]
    and
    [tex]\sum{j= 1}^3((x_1y_1)(x_2y_2))= \sum_{j=1}^3 (-3)(2)(2)(4)= \sum_{j=1}^3 48= 3(48)= 144[/tex]

    But I suspect you meant
    [tex]\prod_{j=1}^3\sum_{i= 1}^2 x_iy_j[/tex] and
    [tex]\sum{j=1}^3\Pi_{i=1}^2 x_iy_j[/tex]

    The first of those is
    [tex]\prod_{j=1}^3(x_1+ x_2)y_j= (x_1+ x_2)\prod_{j=1}^3y_i= (x_1+ x_2)(y_1y_2y_3)[/tex]
    surely you can do that arithmetic yourself.
     
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