Let B (1, x + 3, (x – 1)², 5æ³ ) be an ordered basis for P3. Find the coordinate vector of f(x) = 6x3 – 4x² + 7x – 8 relative to B. fB =

Q: Let B be the basis of P, consisting of the Hermite polynomials 1, 2t, - 2+ 4t, and - 12t + 8t°; and…

A: Consider the Equation

Q: Let B = {1, x, x², x*} be an ordered basis for P3. Find the coordinate vector of f(x) = 4x3 – 72² +…

A: ANSWER:

Q: , find the change-of-coordinates matrix from the basis B= {1– 2t +t?,3 - 5t + 41,2- 2t + 5t?} to the…

A:

Q: Let B be the standard basis of P₁, and consider the basis B' [T]B¹,B. = {(1)· (9)}< of V. Find

A:

Q: 14. The set B = {1 – t²,t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) =…

A: Given vector is: Pt=1+3t-6t2 Basis set for the vector is given as: B=1-t2, t-t2, 2-t+t2 Then, let…

Q: B = {1+t²,t +t?, 1+2t +t²} is a basis for P2. Find the coordinate vector of p(t) = 1 + 4t +7t²…

A:

Q: Let p = 5x + 10x + 3. Find the coordinate vector of p relative to the following basis for P2, P1 =…

A:

Q: Let B = {1+t, t – t2, 2t + t2} be a basis for P2. Find [-3+t – t°]B. %3D

A:

Q: 1) Let T a b la + 2b +2c + 1d + 7e+ (-1) f la + 2b + 4c + 4d +21e+(-2)ƒ la + 2b +3c+ 2d + 12e + (-2)…

A:

Q: Prove that the components of a vector x in a given basis {ê¿} are unique. That is, show that if you…

A: We will prove the given statement.

Q: Let S = y1 be a basis of R and x = E R4. What are the coordinates of x with %3D >Y2 = respect to the…

A:

Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

A:

Q: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

A:

Q: Suppose p= 5x?+2x +3o figure out the coor olicuate relative to the follewing basis for 29 pi =i, Pz…

A: Given p=5x2+2x+3 and basis  p1=1p2=1+xp3=1+x+x2

Q: Y1 Y2 ER3 [Y3. (x, y) 2x1y1 + X2Y2+5x3Y3, for x = |X3 (a) Find a basis for the orthogonal complement…

A:

Q: 2

A:

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R, T(x, y) = (4x – 3y, 5x), B' = {(-2,…

A: We have to find the matrix A' for T relative to the basis B'.

Q: Let B be the basis of P3 consisting of the Hermite polynomials 1, 2t, - 2 + 4t“, and - 12t + 8t°;…

A:

Q: 1. Find the coordinates of vector w (1,2, 3) in the basis A which consists of T1 = (1, 1, 0), 72 =…

A:

Q: Let B be the basis of P2 consisting of the Laguerre polynomials 1, 1 -t, 2 – 4t + t2, and let p(t) =…

A: Let β=1,1-t,2-4t+t2 be the basis for P2R For Pt∈P2R , can be written as linear combination of…

Q: Find the coordinate vector of p(x) = 3 - x + 4x2 with respect to the basis B = {1, 1 + x, -1 + x2}…

A:

Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

A:

Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (-8x + y, 8x – y), B' =…

A:

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = - 823 6x? –…

A: ANSWER :

Q: The set B = is a basis for R2. Find the coordinates of the vector x = -6 relative to the basis B.…

A:

Q: 1. Find [p]a, relative to the basis 3 = {P1. P2: Ps} for P, where p = 4- 3x +x², P1 = 1, P2 = X, P3…

A: Given

Q: The set B= {1-t,t-t,1- 2t-t} is a basis for P2. Find the coordinate vector of p(t) = 1+ 5t – 4t…

A:

Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (−3x + y, 3x − y), B′ = {(1,…

A:

Q: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to…

A:

Q: Find x with respect to the standard basis corresponding to the coordinate vector [x] and basis B. B…

A:

Q: The set B = {1+t²,t +t²,1+ 2t + t?} is a basis for P2. Find the coordinate vector of p(t) = 1+ 4t +…

A:

Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. -4 [x] B% =…

A:

Q: then the second coordinate of the vector in the basis is: (3,5,7) If B=((1,1,1),(1,0, 1), (0,1, 1))…

A:

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2-4t+t, and let…

A:

Q: Let s = {(r² –3r+4, 2r-5, x²+1} be a basis for P2, let q E P2. If (q). = [2,-3, 1], then q = %3D %3D…

A:

Q: Find the coordinate vector of Prelative to the basis S = {P,P2P3} P1 = 1+ x + x, P2 = x + x²,P3 =…

A: Vector

Q: - - The set B = {x² - 2, 4x² − (8 + 3x), 15x² − (28 + 9x)} is a basis for P₂. Find the coordinates…

A:

Q: Find the coordinate vector of p(x) = 5 - 2x + 4x² with respect to the basis B = (1 + x, 1 – X, x?}…

A:

Q: Let B = Note that B is a basis for R?. (You do not need to prove this. (a) Find the…

A: ANSWER :

Q: .2 The set B= {1 +t,-t-t,1+2t+t} is a basis for P,. Find the coordinate vector of p(t)= -3-5t-6t…

A:

Q: 2) Find the coordinate vector [x]p of x relative to the basis B={b1, b2}: [-3] bị = G.b2 = x =G

A:

Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Here we have to change the coordinates of x from given basis B to standard basis S.

Q: B = {3 – 3x, 9 – 2x – 9x², 13 – 4x – 12x?} is a basis for P2. The coordinate vector of p(x) = 4 + 2x…

A: We have to find the coordinate vector of P(x)=4+2x-6x2. w.r.t the basis…

Q: Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find…

A: Given basis are e1,e2,e3 of R3 where e1=1,1,1e2=1,1,-1e3=1,-1,-1 Its dual basis are f1,f2,f3 We have…

Q: Let B = (1, x + 2, (* – 1)", 9x) be an ordered basis for Pg. Find the coordinate vector of f(æ) = 8a…

A: Answer

Q: 1. Find [p]8, relative to the basis B = {p1, P2, P3} for P2 where p = 4 – 3x + x², p1 = 1, p2 = X,…

A: Q1. p = 4 - 3x + x² = (4)p1 + (-3)p2 + (1)p3  So, [p]β = [4   -3   1]

Q: a) Find the coordinate vector of x = of R³. To with respect to the ordered basis *- {0-1-8} E [x] E…

A: as per the guidelines I am answering only first question (a) Let the coordinate vector of x=2-40…

Q: If g and R. are bases of a vector space y and -21 is the matrix of transition from the basis a to…

A:

Q: Suppose T E L(V, W), and w1, ..., wm is a basis of range T.

A: Given that T∈L(V,W)andw1,.......wm is a basis of range T.To prove there exist…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.