linear algebra: 18. (5 points) Define the linear transformation D: PPby D(p(x)) = p'w). Find the...
Define the linear transformation D: P3 → P2 by D(p(x))=p'(x). Find the standard matrix for this linear transformation (using the standard basis for P3 and P2).
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) =...
linear algebra Let T: P2 - P4 be the linear transformation T() = 2x2p. Find the matrix A for T relative to the bases B = {1, x,x?) and B' = {1, x,x2, x3, x4} A=
linear algebra Find the standard matrix for the linear transformation T. T(x, y, z) = (6x – 8z, 8y - z) BE
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...
subject: Linear Algebra if someone could answer and explain why the answers are correct that would be much appreciated. Thanks in advance!! Exercises 1. The set P2 of polynomials of degree less than or equal to two is a vector space under polyno- mial addition and scalar multiplication by real numbers. (a) (5 points) Show that the set A = {1, 2, 22) is a basis for P2. (b) (2 points) Find the coordinate vector of an arbitrary polynomial of...
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.
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...
linear algebra help 4.) (18 points) let A = [ag]nzn- Define WA (B e Mnn BA = AB). Determine whether WA is a subspace of Mn,n with the standard operations of matrix addition and scalar multiplication.
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 {1,x,x} and {1, 1-x}. 6 b) For the vector, p(x) = 2x + x - 2 (i) 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 {1,x,x"}. (ii) Show that...