Linear Combination

**AkilMAI** · January 30th 2011, 02:13 PM

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

**dwsmith** · January 30th 2011, 02:22 PM

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

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

Then it is simple $v_1+v_2+v_3=p(x)$

**HallsofIvy** · January 30th 2011, 03:27 PM

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.

**dwsmith** · January 30th 2011, 03:28 PM

Originally Posted by HallsofIvy

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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