Matrix associated with a linear map

**kjchauhan** · November 9th 2009, 07:26 AM

Determine the matrix $(T:B_1,B_2)$ for linear map $T: \wp_{4} {\longrightarrow}\wp_{4}$ , $T(p)(x) =\int_{1}^{x} \ p'(t) \ dt$
Where $B_1={\{1, x, x^2, x^3, x^4}\}$ and $B_2={\{x-1,x+1,x^2-x^4,x^3-x^4,x^2+x}\}$ .

Solution please..

Thanks..

**tonio** · November 9th 2009, 07:31 AM

Originally Posted by kjchauhan

Determine the matrix $(T:B_1,B_2)$ for linear map $T: \wp_{4} {\longrightarrow}\wp_{4}$ , $T(p)(x) =\int_{1}^{x} \ p'(t) \ dt$
Where $B_1={\{1, x, x^2, x^3, x^4}\}$ and $B_2={\{x-1,x+1,x^2-x^4,x^3-x^4,x^2+x}\}$ .

Solution please..

Thanks..

Apply T on each and every element of B_1 and write the result as a linear combination of elements of B_2, and then take the transpose of the coefficients matrix.

Tonio

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