Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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Step 1: Write the theorems
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Step 2: Determine kerT
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Step 3: Prove that T is one to one
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Step 4: Determine ImT
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Step 5: Prove that T is onto
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Solution
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