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3. Let T be a linear operator in C² and is defined by T(a, b) = (3a + (2 + i)b, (2 — i)a + 7b) (a) Let 3 be a standard ordered basis of C², please find the matrix representation 4 of T. (b) What kind of operator is T: (1) Normal, (2) Self-adjoint, (3) Unitary, (4) Orthogonal projection? You must provide enough evidence of your answer to get the full credit. (c) Please find an orthonormal basis of V consisting eigenvectors of T.

3. Let T be a linear operator in C² and is defined by T(a, b) = (3a + (2 + i)b, (2 — i)a + 7b) (a) Let 3 be a standard ordered basis of C², please find the matrix representation 4 of T. (b) What kind of operator is T: (1) Normal, (2) Self-adjoint, (3) Unitary, (4) Orthogonal projection? You must provide enough evidence of your answer to get the full credit. (c) Please find an orthonormal basis of V consisting eigenvectors of 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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3. Let T be a linear operator in C² and is defined by T(a, b) = (3a + (2 + i)b, (2 – i)a + 7b) (a) Let ß be a standard ordered basis of C², please find the matrix representation A of T. (b) What kind of operator is T: (1) Normal, (2) Self-adjoint, (3) Unitary, (4) Orthogonal projection? You must provide enough evidence of your answer to get the full credit. (c) Please find an orthonormal basis of V consisting eigenvectors of T.
Transcribed Image Text:3. Let T be a linear operator in C² and is defined by T(a, b) = (3a + (2 + i)b, (2 – i)a + 7b) (a) Let ß be a standard ordered basis of C², please find the matrix representation A of T. (b) What kind of operator is T: (1) Normal, (2) Self-adjoint, (3) Unitary, (4) Orthogonal projection? You must provide enough evidence of your answer to get the full credit. (c) Please find an orthonormal basis of V consisting eigenvectors of T.
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