Consider the basis B = {({2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B.Then for an arbitrary pair (c, d) EV, the set {x1(c, d), x2(c,d)) is equal to:{(3d-c), (c-2d)}{(3d+ c), (c+ 2d)}{(2d-c), (c + 3d)}{(2d+c), (c + 3d)}{(3d+c), (2c - d)}

Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Answered: Consider the basis B = {(2, 1), (3, 1}}…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

a) Show that the set of vectors are orthogonal vectors in R3 U1 = (1, -2, 3), u2 = (1, 2, 1) and u3 (-8, 2, 4) %3D %3D b) Write W = (13, -4, 7) as linear combination of the orthogonal basis.
Let -----[B]---[B)-----] 2 = = 4 -7 and 3 2 Explain that B = (V1, V2, V3) forms a basis of a 3-dimensional space. Find [u] (the coordinate of u with respect to the basis B) by writing the vector u as a linear combination of 7₁, 72, and v3.
: Let p 8x2 + 4x + 3. Find the coordinate vector of p relative to the following basis for P2, 1, p2 = 1+x, P3 = 1+x+x².
Consider the basis B of R2 consisting of vectors and 2 Find in R² whose coordinate vector relative to the basis B is [] B TH = =
Find the coordinate vector of v = [-7 [-7 [011], [221] ). −4 -4 -5] relative to the ordered basis B = ([101], VB =
2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. Then find a basis for each set and give the dimension. (a) W is the set of vectors of the form (3s, -2s, s). (b) W is the set of vectors of the form (t – 2, 0,6 – 3t). (c) H is the set of vectors of the form (2b, a, 3b) (d) H is the set of vectors of the form (-b+ 2c, b, 4c),
Find the representation of (9, -2, -3) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (9, -2, -3) in terms of the ordered basis B = {i,j,k}. [(9,-2,-3)]B= b. Represent the vector (9, -2, -3) in terms of the ordered basis C = {3, e1, e2}. [(9,-2,-3)] c = c. Represent the vector (9, -2, -3) in terms of the ordered basis D= {-2, -1, e3}. [(9,-2,-3)]D =
The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v = (1,0,1); w= (0,0,1) } is: O A. (1,-4,3) OB. (-4,3,1) OC. (3,- 7,5) O D. (2,-1,1)
Given basis B = {(1, -1), (2, 3)} and basis C = {(1, 0), (0, 1)}, and linear map T = (x + 2y ; 2x - y) from R2 --> R2, find the coordinate vectors of basis C in terms of basis B.
Find the coordinates of x = {-10, 2, 4} with respect to the basis consisting of u, {1, 3, 2}, u, = {2, 1, 4}, and u; = {1,0, 6}. -
Explain how fixing a basis v1, · · , Vn of V associates to a quadratic form a corresponding function in n variables of the form q(x1,· . for a certain symmetric matrix A = (aj). , Xn) = Li=1 aijXiXj, .
a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x) = -3x² + 2x – 5 , and q(x) = -x+5x? b) Verify that the basis set S = {(3,0,4), (-4,0,3), (0,1,0)} is orthogonal then find the coordinates of the vector u = (-5,5,1) using inner product

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Consider the basis B = {(2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for an arbitrary pair (c, d) EV, the set {x1(c, d), x2(c, d)} is equal to: {(3d-c), (c-2d)} {(3d+ c), (c+ 2d)} {(2d-c), (c + 3d)} {(2d+c), (c + 3d)} {(3d+c), (2c-d)}