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Let t be the linear transformation t: R² → R² (x, y) (7x26y, 13x + 20y). (a) Find the matrix A of t with respect to the standard basis for the domain and the codomain. (b) Without using the characteristic equation of A, verify that (1, 1) and (2,-1) are eigenvectors of A, and state the corresponding eigenvalues. (c) By using Theorem C59, write down the matrix B of t with respect to the eigenvector basis E = {(1, 1), (2, -1)} for the domain and the codomain. 4 2 = with (d) The linear transformations: R² →R² has matrix C respect to the basis E for the domain and the codomain. Find the matrix of] tos with respect to the basis Ę for the domain and the codomain.

Let t be the linear transformation t: R² → R² (x, y) (7x26y, 13x + 20y). (a) Find the matrix A of t with respect to the standard basis for the domain and the codomain. (b) Without using the characteristic equation of A, verify that (1, 1) and (2,-1) are eigenvectors of A, and state the corresponding eigenvalues. (c) By using Theorem C59, write down the matrix B of t with respect to the eigenvector basis E = {(1, 1), (2, -1)} for the domain and the codomain. 4 2 = with (d) The linear transformations: R² →R² has matrix C respect to the basis E for the domain and the codomain. Find the matrix of] tos with respect to the basis Ę for the domain and the codomain.

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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Let t be the linear transformation t: R² → R² (x, y) (7x26y, 13x + 20y). (a) Find the matrix A of t with respect to the standard basis for the domain and the codomain. (b) Without using the characteristic equation of A, verify that (1, 1) and (2,-1) are eigenvectors of A, and state the corresponding eigenvalues. (c) By using Theorem C59, write down the matrix B of t with respect to the eigenvector basis E = {(1, 1), (2, -1)} for the domain and the codomain. 4 2 = with (d) The linear transformations: R² →R² has matrix C respect to the basis E for the domain and the codomain. Find the matrix of] tos with respect to the basis Ę for the domain and the codomain.
Transcribed Image Text:Let t be the linear transformation t: R² → R² (x, y) (7x26y, 13x + 20y). (a) Find the matrix A of t with respect to the standard basis for the domain and the codomain. (b) Without using the characteristic equation of A, verify that (1, 1) and (2,-1) are eigenvectors of A, and state the corresponding eigenvalues. (c) By using Theorem C59, write down the matrix B of t with respect to the eigenvector basis E = {(1, 1), (2, -1)} for the domain and the codomain. 4 2 = with (d) The linear transformations: R² →R² has matrix C respect to the basis E for the domain and the codomain. Find the matrix of] tos with respect to the basis Ę for the domain and the codomain.
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