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Math Help - Linear Combination

  1. #1
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    Linear Combination

    How can I write this expression as a linear combination of three
    vectors (polynomials) in P3 p(x) = a + bx + cx^2 +(-a-c)x^3?
    Thank you
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  2. #2
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    Quote Originally Posted by AkilMAI View Post
    How can I write this expression as a linear combination of three
    vectors (polynomials) in P3 p(x) = a + bx + cx^2 +(-a-c)x^3?
    Thank you
    Let your vectors be

    \{a+bx, \ cx^2, \ -(a+c)x^3\}

    Then it is simple v_1+v_2+v_3=p(x)
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  3. #3
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    dwsmith is right, that is a linear combination, but I suspect what they want is a + bx + cx^2 +(-a-c)x^3= a(1- x^3)+ bx+ c(x^2- x^3) where "a", "b", and "c" are the coefficients of the linear combination.
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    dwsmith is right but I suspect what they want is a + bx + cx^2 +(-a-c)x^3= a(1- x^3)+ bx+ c(x^2- x^3)
    I like to go with the simpliest answer.
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