Problem #11 : Let p-7x2 + 5x + 4 Find the coordinate vector of p relative...
assign 11 105: Problem 9 Previous Problem Problem List Next Problem (1 point) Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to 2. Let C (-3,-1- 3x,-1 + 2x - 3x2] be an ordered basis for P2 a. Write 23x -9x2 as a linear combination of elements from the basis C 2+3x-9x2- (-1 + 2x - 3x2) b. Let [glc denote the coordinate representation of q relative to the...
Prob. 4 (12.5 pts) The set of vectors S = {p1.p2.p3 } may be a basis for P2 p1 = 1 + x + x2 p2 = x + x2 p = x² a) Verify that this is the case. b) If it is a basis, find the coordinate vector of b relative to S. b = 7 - x + 2 x2
6. Let :P - P be the linear operator defined as (p(x)) - (5x), and let B = (1.x.x) be the standard basis for P2 a.) (5 points) Find the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x Determine (px)then find (p(x)) using (Tle from parta c.) (1 point) Check your answer to part b by evaluating T(x+6x) directly
Find the coordinate vector
Find the coordinate vector [X]e of x relative to the given basis B = {b1,b2,63). [x]8 = (Simplify your answers.)
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
3) Let T: P2 → P3 be such that T (p) = 2p(x) - xp(x). Let Sy be the standard basis for P, and S, the standard basis for Pz. a) Find T (2 + 5x). b) Find [T(S)]sz: c) Use [T(S)]s to find [T(3 – x2)]sz. d) Verify that Vp € P2, [T (p)]sz = [T(S)][p]sz:
Answer Question #12. Question #11 is only for reference
11. Let po, pi, and p2 be the orthogonal polynomials described in Example 5, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, and 2. Find the orthogonal projection of tonto Span {po, pi, p2). 12. Find a polynomial p3 such that {po, p1, p2.p3} (see Exercise 11) is an orthogonal basis for the subspace P3 of P4. Scale the polynomial p3 so that its...
Let B={(4,0), (0,3)} and v = (12,6). Find [v]_B, the coordinate vector of v, relative to basis B. (To enter a height 2 column vector, use the notation (a,b)^T.)
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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...
Find the coordinate vector [x]g of x relative to the given basis B = {by, by, b}. 1 4 1 5 b = 0 bz 1 1 2 5 [x]g - (Simplify your answer.)