# Linear Combination

• Jan 30th 2011, 02:13 PM
AkilMAI
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
• Jan 30th 2011, 02:22 PM
dwsmith
Quote:

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

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

Then it is simple \$\displaystyle v_1+v_2+v_3=p(x)\$
• Jan 30th 2011, 03:27 PM
HallsofIvy
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.
• Jan 30th 2011, 03:28 PM
dwsmith
Quote:

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.