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)}

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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

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Let B be the standard basis of the space P, of polynomials.Use coordinate vectors to test whether the following set of polynomials span P,. Justify your conclusion. 1-2t + 3, -4+6t – 81, -2+3t - 4?, 2- 3t + 412 Does the set of polynomials span P,? O A. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R°. By isomorphism between R and P, , the set of polynomials does not span P,. O B. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between R3 and P, , the set of polynomials spans P2- O C. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R2. By isomorphism between R2 and P,, the set of polynomials does not span P,. O D. Yes;…
B = (f1, f2, f3) is a basis for R2[] where fi = 1+ 2x + a², f2 = 2+ 3r + 2x², f3 = 2 + x +3x². If [g]8 = then g = 1 a) 1– r +x² b) a c) 2r² d) 1+ x² e) 1+ 2r².
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)}
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.
find representation of the vector v=2-2x+6x2 with respect to following basis
Show that the set S = {(4,3, 2), (0, 3, 2), (0,0, 2)} is a basis for R* by showing that it spans R³ and is linearly independent. Then, express the vector x = (8, 3, 8) as a linear combination of the vectors from S.
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 = =
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let az = (2,-1.0), az1 = (0,1,2), az2 = (1,-1,3) in R³ space. %3D a) Can the vector (7,-6,7) be written as a linear combination of vectors a, az1, az2? Please review. b) Examine whether the set {a1, a2, a3} is a basis of R3.
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)
Create a basis of R¹ containing vectors (1,-1,3, 2) and (2,1,3, 4) by adding basis vectors of the orthogonal comlement to their span.
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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)}