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2). For the following linear transformations T: R → R², where Ti(r, y) = (2x + 3y, 5x – y) T2 : R → R², where T2(r, y) = (3x + y, x – 3y) a). Show that T1 and T2 are one-to-one and onto. b). Find formulas for T (x, y), T,'(r, y) and (T2 o T1)-'(x, y) c). Check whether that (T2 o T1)- = T¡' o T,'.

2). For the following linear transformations T: R → R², where Ti(r, y) = (2x + 3y, 5x – y) T2 : R → R², where T2(r, y) = (3x + y, x – 3y) a). Show that T1 and T2 are one-to-one and onto. b). Find formulas for T (x, y), T,'(r, y) and (T2 o T1)-'(x, y) c). Check whether that (T2 o T1)- = T¡' o T,'.

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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2). For the following linear transformations T: R → R², where Ti(r, y) = (2x + 3y, 5x – y) T2 : R → R², where T2(r, y) = (3x + y, x – 3y) a). Show that T1 and T2 are one-to-one and onto. b). Find formulas for T (x, y), T,'(r, y) and (T2 o T1)-'(x, y) c). Check whether that (T2 o T1)- = T¡' o T,'.
Transcribed Image Text:2). For the following linear transformations T: R → R², where Ti(r, y) = (2x + 3y, 5x – y) T2 : R → R², where T2(r, y) = (3x + y, x – 3y) a). Show that T1 and T2 are one-to-one and onto. b). Find formulas for T (x, y), T,'(r, y) and (T2 o T1)-'(x, y) c). Check whether that (T2 o T1)- = T¡' o T,'.
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