Thanks?
(3) (a) Recall the basis {x2 +1, 2+1, x2 + x + 1} for P2 in Problem 1. What is the coefficient vector of x2 – 3 +1 in this basis? (b) What is the coefficient vector of x2 – x +1 in the standard basis for P2?
Let T: P2 --> R2 be the linear transformation such that T(x+1)=(1,1), T(x2)=(1,0) and T(x-1)=(0, 1). Find T(2+x+x2).
Let S = {t2.t-1,1} be an ordered basis for P2(t). If the vector v in P2(6) has the coordinate vector 2 3 with respect to S, then what is the vector v? Select one: O at2 + 2t +1 O b. +2 +1+1 O c. 12 + 2t - 1 O d. t2 + 2t
Let S={2,3+x,1−x2}, p(x)=2−x−x2 and V=P2 (a) If possible, express p(x)as a linear combination of vectors in S. (b) By justifying your answer, determine whether the set S is linearly independent or linearly dependent. (c) By justifying your answer, determine whether the set S is a basis for P2 Please solve it in very detail, and make sure it is correct.
NEED (B) AND (C)
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of continuous real-valued funo- tions on the domain [-1, 1] (b) Use the Gram-Schmidt process to find an orthonormal basis for P2(R) with re- spect to this inner product (c) Find a polynomial q(x) such that for every p E P2R
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space...
Let S = {2,3 + x, 1 – x2}, p(x) = 2 - x - x2 and V = P2. (a) If possible, express p(x) as a linear combination of vectors in S. (b) By justifying your answer, determine whether the set S is linearly independent or linearly dependent. (c) By justifying your answer, determine whether the set S is a basis for P2.
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
The vectors X1 = = (1, -1 -1,1,-1) and X2 = = (1,1, -1, -1)7 form an orthonormal set in R4. Let 1 -1 1 -1 A= 1 -1 -1 (a) Extend the set {x1, x2} to an orthonormal basis for R4 by finding an orthonormal basis for the null space N(A) of A. (b) Give the QR-decomposition for AT.
The vectors X1 = = (1, -1 -1,1,-1) and X2 = = (1,1, -1, -1)7 form an orthonormal set in R4. Let 1 -1 1 -1 A= 1 -1 -1 (a) Extend the set {x1, x2} to an orthonormal basis for R4 by finding an orthonormal basis for the null space N(A) of A. (b) Give the QR-decomposition for AT.
1. Let B { 1, х, хг} et S {x2 +x, 2-1, x+1 } be two basis of P2. Let T : P2 P2 be a linear transformation such that 3,S 2 2 -2 Find a basis of Ker(T), a basis of Im(T) and T^b 2. Let Let : P1 → P1 be a linear transformation such that 4 -3 where B-[1, x,} et S - {2c - 1,x - 1} be two basis of P1. Find A2 and T2....