Linear Transformation: Bmatrix [T]Bby PirateFan308 Tags: bmatrix, linear algebra, transformations 

#1
Dec611, 06:01 PM

P: 94

1. The problem statement, all variables and given/known data
Let V be polynomials, with real coefficients, of degree at most 2. Suppose that [itex]T:V→V[/itex] is differentiation. Find the [itex]B[/itex]matrix [T]_{B} if B is the basis of V B = {1+x, x+x^{2}, x} 2. Relevant equations For [itex]T:V→V[/itex] the domain and range are the same [T]_{B} is the matrix whose ith column is [itex][T(vi)]_B[/itex] [itex][T(v)]_C = A[v]_B[/itex] where [itex]A=[T]_B[/itex] 3. The attempt at a solution So because the degree can be at most 2, the polynomials will be of the form a+bx+cx^{2}. This can be denoted using a(1+x)+c(x+x^{2})+(bac)(x). It will turn into a+bx (because we take the derivative, we take powers to a max of 1) and we would say a(1+x)+0(x+x^{2}+b(x). After this, I'm not sure how to find the Bmatrix, as I'm a bit confused as to what it is exactly. 



#2
Dec611, 09:44 PM

P: 366





#3
Dec711, 06:01 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,904

What is T(1+ x)? What is T(x+ x^2)? What is T(x)?
Write each of those as a linear combination of 1+ x, x+ x^2, and x and the coefficients are the columns of your matrix. 


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