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Show that each linear operator T on R2 is nonsingular and find a formula for T- , where (a) T(x,y) = (x + 2y, 2x + 3y), (b) T(x,y) = (2x – 3y, 3x – 4y).

Show that each linear operator T on R2 is nonsingular and find a formula for T- , where (a) T(x,y) = (x + 2y, 2x + 3y), (b) T(x,y) = (2x – 3y, 3x – 4y).

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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I need to solve the question (5.79) (b)
5.79. Show that each linear operator T on R² is nonsingular and find a formula for T-, where (a) T(x,y) = (x + 2y, 2x+ 3y), (b) T(x,y) = (2x – 3y, 3x – 4y). 5.80. Show that each of the following linear operators T on R' is nonsingular and find a formula (а) Т(х, у, 2) — (х — Зу — 2, у— 4z, 2); (b) Т(х,у, 2) — (х + z, х —у, у).
Transcribed Image Text:5.79. Show that each linear operator T on R² is nonsingular and find a formula for T-, where (a) T(x,y) = (x + 2y, 2x+ 3y), (b) T(x,y) = (2x – 3y, 3x – 4y). 5.80. Show that each of the following linear operators T on R' is nonsingular and find a formula (а) Т(х, у, 2) — (х — Зу — 2, у— 4z, 2); (b) Т(х,у, 2) — (х + z, х —у, у).
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