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. Define a linear transformation T: R² → R² by ere G = 3)₁0<0< cos (0) -sin(0) cos(0) cos(0) T(x) = Gx-x, <<. Then linear transformation T is one-to-one and onto.

. Define a linear transformation T: R² → R² by ere G = 3)₁0<0< cos (0) -sin(0) cos(0) cos(0) T(x) = Gx-x, <<. Then linear transformation T is one-to-one and onto.

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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(3). Define a linear transformation T: R2 R2 by →> where G = cos (0) - sin(0) cos(0) cos(0) 3) ₁ 0 <0< satisfies the equation A² - (a + d) A+ (ad - bc)I = 0, for any real numbers T(x) = Gx-x, a b 0. Then linear transformation T is one-to-one and onto. ( ) (4). The matrix A = C d a, b,c and d, where O denotes a 2 x 2 square matrix. distinot piconvalues then so does 4².
Transcribed Image Text:(3). Define a linear transformation T: R2 R2 by →> where G = cos (0) - sin(0) cos(0) cos(0) 3) ₁ 0 <0< satisfies the equation A² - (a + d) A+ (ad - bc)I = 0, for any real numbers T(x) = Gx-x, a b 0. Then linear transformation T is one-to-one and onto. ( ) (4). The matrix A = C d a, b,c and d, where O denotes a 2 x 2 square matrix. distinot piconvalues then so does 4².
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