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