MAT280 Fall2020 TakeHome 119 update (1) - WordRiley CyronInsertDesignLayoutReferencesMailingsReviewViewHelp6.Let å =(first two ID digits), b= 7 (middle three ID digits), č =| 1(last two digits)Let u =(first three digits), v =(last four digits)1Let A =1221 5 7 4 95 7 4 9 1(place your whole ID in each row)Calculations.1. Consider the basis B = {(2,–v2), (2, V2)} for R². Define (3,2) =y121 +2.a) Verify that B is an orthonormal basis.b) Calculate [wl, for w = (20,-6v2).2. Define a linear transformation T: R → R² by T(x) = Ax.a) Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2).b) Calculate the pre-image of (60, 120).c) Determine a basis of the range of the transformation.d) Determine a basis for the kernel of the transformation.3. Define T: R → R³ such that T(a) = (1,2,1), T(b) = (0,1,3), T(C) = (1,0,–1).Calculate T(-2,3, -1).4. Define T: R² → R² by T(x, y) = (3x – 2y, y – 2x).a) Construct the standard matrix for T.b) Construct the matrix for T relative to the basis {(5,2), (2,1)}.c) Construct the matrix for T-1 relative to the basis {(1,1), (1,2)}.TFogus目

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Answered: 1. Consider the basis B = {(2, –v2),…

1. Consider the basis B = {(2, –v2), (2, V2)} for R². Define (ỷ, 2) =y,2 +y22. %3D a) Verify that B is an orthonormal basis. b) Calculate [w], for w = (20, –6V2).

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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Question

MAT280 Fall2020 TakeHome 119 update (1) - Word
Riley Cyron
Insert
Design
Layout
References
Mailings
Review
View
Help
6.
Let å =
(first two ID digits), b
= 7 (middle three ID digits), č =| 1
(last two digits)
Let u =
(first three digits), v =
(last four digits)
1
Let A =
12
2
1 5 7 4 9
5 7 4 9 1
(place your whole ID in each row)
Calculations.
1. Consider the basis B = {(2,–v2), (2, V2)} for R². Define (3,2) =y121 +2.
a) Verify that B is an orthonormal basis.
b) Calculate [wl, for w = (20,-6v2).
2. Define a linear transformation T: R → R² by T(x) = Ax.
a) Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2).
b) Calculate the pre-image of (60, 120).
c) Determine a basis of the range of the transformation.
d) Determine a basis for the kernel of the transformation.
3. Define T: R → R³ such that T(a) = (1,2,1), T(b) = (0,1,3), T(C) = (1,0,–1).
Calculate T(-2,3, -1).
4. Define T: R² → R² by T(x, y) = (3x – 2y, y – 2x).
a) Construct the standard matrix for T.
b) Construct the matrix for T relative to the basis {(5,2), (2,1)}.
c) Construct the matrix for T-1 relative to the basis {(1,1), (1,2)}.
TFogus
目

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