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Q. 3. A transformation T:R² →R² first reflects vectors through the y axis, and then rotates vectors by 3 a. Find the matrix of the transformation T. b. Find the inverse transformation of T , if exists. c. Draw the transformation T for x =

Q. 3. A transformation T:R² →R² first reflects vectors through the y axis, and then rotates vectors by 3 a. Find the matrix of the transformation T. b. Find the inverse transformation of T , if exists. c. Draw the transformation T for x =

Advanced Engineering Mathematics
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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Q. 3. A transformation T: R² →R² first reflects vectors through the y axis, and then rotates vectors by 3 a. Find the matrix of the transformation T. b. Find the inverse transformation of T , if exists. -1 c. Draw the transformation T for x =| 2
Transcribed Image Text:Q. 3. A transformation T: R² →R² first reflects vectors through the y axis, and then rotates vectors by 3 a. Find the matrix of the transformation T. b. Find the inverse transformation of T , if exists. -1 c. Draw the transformation T for x =| 2
Q. 7. Is the power set P(H), which is the set of all subset of H = {1, 2} with the operations of * and *' a Boolean algebra? Justify your answer. Here the operations * and *' on P(H) are defined by: C*D=(CUD)-(CND), and C*' D =(CND), for all C,De P(H). Here U and N represent union and intersection, respectively. Q. 8. Show that (Z,,+6,×6) is a commutative ring. Is (Z.,+6,×6) a field? Justify your answer. Q. 9. List two famous mathematicians and discuss their contributions in mathematics.
Transcribed Image Text:Q. 7. Is the power set P(H), which is the set of all subset of H = {1, 2} with the operations of * and *' a Boolean algebra? Justify your answer. Here the operations * and *' on P(H) are defined by: C*D=(CUD)-(CND), and C*' D =(CND), for all C,De P(H). Here U and N represent union and intersection, respectively. Q. 8. Show that (Z,,+6,×6) is a commutative ring. Is (Z.,+6,×6) a field? Justify your answer. Q. 9. List two famous mathematicians and discuss their contributions in mathematics.
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