Define the linear transformation D: P3 → P2 by D(p(x))=p'(x). Find the standard matrix for this...
linear algebra: 18. (5 points) Define the linear transformation D: PPby D(p(x)) = p'w). Find the standard matrix for this linear transformation (using the standard basis for P3 and P2).
could u help me for this question?thanku!! 21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x2,x) and B={1,1+x, 1 +x+12, 1-x3}. (b) Use [TlB. A to find a basis for the range of T. (c) Use TB.A to find a basis for the kernel of T. (d) State the rank and nullity of T. 21. Let T...
show work pls! Let L :P2 →P3 be the linear transformation given by L(p(t)) = 5p"(t) + 3p' (t) + 1p(t) + 4tp(t). Let E = (e1, C2, C3) be the basis of Pề given by ei(t) = 1, ez(t) = t, ez(t) = 62. and let F = (f1, f2, f3, f4) be the basis of P given by fi(t) = 1, fz(t) = t, f3(t) = ť, fa(t) = {'. Find the coordinate matrix LFE of L relative...
7. (1 pt) Find a basis {p(x),q(x)} for the kernel of the linear transformation L:E P3 x + R defined by L(f(x)) = f'(5) - f(1) where P3 x) is the vector space of polynomials in x with degree less than 3. p(x) = — , 9(x) = Answer(s) submitted: . x
Let T:P2 P2 be the linear transformation defined by T(p(x)) = p(4x + 5) - that is T(CO + C1x + c2x2) = co+C1(4x + 5) + c2(4x + 5)2. Find [7]3 with respect to the basis B = {1, x, x?}. Enter the second row of the matrix [7]z into the answer box below. i.e.. if A = [7]B. then enter the values a21, a22, 223, (in that order), separated with commas.
6. Let T P2 P be a linear transformation such that T P2P2 is still a linear trans formation such that T(1) 2r22 T(2-)=2 T(1) = 2r22 T(12 - )=2 T(x2x= 2r T(r2)2x (a) (6 points) Find the matrix for T in some basis B. Specify the basis that you use. (d) (4 points) Find a basis for the eigenspace E2. (b) (2 points) Find det(T) and tr(T') (e) (4 points) Find a basis = (f,9,h) for P2 such that...
Linear algebra: tell me what happen. How do we get that matrix A by using the D derivative D(x^2)=2x how we get D(x^2)=2x+0*1???? follow the comment EXAMPLE 5 The linear transformation D defined by D(p-p' maps P3 into P2. Given the ordered bases [r.x, and [x, for Ps and P2, respectively, we wish to determine a matrix representation for D. To do this, we apply D to each of the basis elements of P3 Convert t Microso Documen D(x) =...
4) The linear transformation L defined by L(p(x)) = p(x)+p(0) maps Pinto P. a) Find the matrix representation of L with respect to the ordered bases l_r"} and {1, 1-x). b) For the vector, p(x) = 2x' +1-2 () find the coordinates of L(p(x)) with respect to the ordered basis{1, 1-x), using the matrix you found in a). Remember to use the coordinate vector of p(x) with respect to the basis {1x2). (ii) Show that they are the weights that...
let T: P2 --> R be the linear transformation defined by T(p(x))=p(2) a) What is the rank of T? b)what is the nullity of T? c)find a basis for Ker(T)
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a geometrical interpretation of T. 2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a...