Question

Consider Linear transformation in P2(R) T(x)=((1-x2)f'(x))'. Compose a basis for P2(R) composed of eigenvectors of T.

Consider Linear transformation in P2(R) T(x)=((1-x2)f'(x))'. Compose a basis for P2(R) composed of eigenvectors of T.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the vector space P2 := P2(F) and its standard basis α = {1,x,x^2}. 1Prove that...
Consider the vector space P2 := P2(F) and its standard basis α = {1,x,x^2}. 1Prove that β = {x−1,x^2 −x,x^2 + x} is also a basis of P2 2Given the map T : P2 → P2 defined by T(a + bx + cx2) = (a + b + c) + (a + 2b + c)x + (b + c)x2 compute [T]βα. 3 Is T invertible? Why 4 Suppose the linear map U : P2 → P2 has the matrix representation...
Suppose R: |R^2 -> |R^2 is the linear transformation: R( x1 , x2) = (x2 ,...
Suppose R: |R^2 -> |R^2 is the linear transformation: R( x1 , x2) = (x2 , x1) a) Give a geometric description of R. b) Compute the matrix of R relative to te standard basis of |R^2 c) Let v1 = (1, 1) and v2 = (1, -1) Verify that B = (v1, v2) is a basis for |R^2, and compute the matrix of R relative to the basis B, i.e [R]B
Suppose T: P2(R) ---> P2(R) by T(p(x)) = x^2 p''(x) + xp'(x) and U : P2(R)...
Suppose T: P2(R) ---> P2(R) by T(p(x)) = x^2 p''(x) + xp'(x) and U : P2(R) --> R by U(p(x)) = p(0) + p'(0) + p''(0). a. Calculate U composed of T(p(x)) without using matricies. b. Assuming the standard bases for P2(R) and R find matrix representations of T, U, and U composed of T. c. Show through matrix multiplication that the matrix representation of U composed of T equals the product of the matrix representations of U and T.
1   Define by T:P2-P2 is given by T(p(x))=p(x)-p'(x) a. Prove that T is a linear transformation....
1   Define by T:P2-P2 is given by T(p(x))=p(x)-p'(x) a. Prove that T is a linear transformation. b. Show T is one to one. c. If   is given by . Explain why T is not one to one.
Define T : P2 → R3 via T(a+bx+cx2) = (a+c,c,b−c), and let B = {1,x,x2} and...
Define T : P2 → R3 via T(a+bx+cx2) = (a+c,c,b−c), and let B = {1,x,x2} and D ={(1, 0, 0), (0, 1, 0), (0, 0, 1)}. (a) Find MDB(T) and show that it is invertible. (b) Use the fact that MBD(T−1) = (MDB(T))−1 to find T−1. Hint: A linear transformation is completely determined by its action on any spanning set and hence on any basis.
Consider the transformation, T : P1 → P2 defined by T(ax + b) = ax2 +...
Consider the transformation, T : P1 → P2 defined by T(ax + b) = ax2 + ax + a (a) Find the image of 2x + 1. (b) Find another element of P1 that has the same image. (c) Is T a one-to-one transformation? Why or why not? (d) Find ker(T) and determine the basis for ker(T). What is the dimension of kernel(T)? (e) Find range(T) and determine a basis for range(T). What is the dimension of range(T)?
Determine whether or not the transformation T is linear. If the transformation is linear, find the...
Determine whether or not the transformation T is linear. If the transformation is linear, find the associated representation matrix (with respect to the standard basis). (a) T ( x , y ) = ( y , x + 2 ) (b) T ( x , y ) = ( x + y , 0 )
consider the basis S={v1,v2} for R^2,where v1=(-2,1) and v2=(1,3),and let T:R^2-R^3 be linear transformation such that...
consider the basis S={v1,v2} for R^2,where v1=(-2,1) and v2=(1,3),and let T:R^2-R^3 be linear transformation such that T(v1)=(-1,2,0) And T(v2)=(0,-3,5), find T(2,-3)
Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T...
Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an orthogonal matrix ?I any case,find the eigen values and eigen vectors of A .
let T: P3(R) goes to P3(R) be defined by T(f(x))= xf'' (x) + f'(x). Show that...
let T: P3(R) goes to P3(R) be defined by T(f(x))= xf'' (x) + f'(x). Show that T is a linear transformation and determine whther T is one to one and onto.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT