Problem 0.3 A = Consider a 2 x 2 matrix A and v, wE R² -8₁ -0 -1 3 2 (1) Find all eigenvectors of A. (2) Find [A]g with respect to the ordered basis B = (v, w) (3) Give an explicit formula for An. ¹Think about what it means geometrically, in relation with the shearing map from problem 0.2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Can I have help solving problem 0.3? (Problem 0.2 is only attached as a reference to the footnote)
Consider a 2 x 2 matrix
1
U
01
(1) Compute U², U³, and give an explicit formula for Un.
Problem 0.2
(2) Let Lu : R² → R² be the linear transformation given by Lu()
Uz. For a given unit square
S = {(x, y): 0 ≤ x, y ≤ 1},
sketch the image Lu (S) of S.
(3) Is U diagonalizable?
Transcribed Image Text:Consider a 2 x 2 matrix 1 U 01 (1) Compute U², U³, and give an explicit formula for Un. Problem 0.2 (2) Let Lu : R² → R² be the linear transformation given by Lu() Uz. For a given unit square S = {(x, y): 0 ≤ x, y ≤ 1}, sketch the image Lu (S) of S. (3) Is U diagonalizable?
Problem 0.3
A =
Consider a 2 x 2 matrix A and v, w€ R²
1 4
--- ---
2
(1) Find all eigenvectors of A.
(2) Find [A]Â with respect to the ordered basis B = (v, w)
(3) Give an explicit formula for An.
¹Think about what it means geometrically, in relation with the shearing map from
problem 0.2
Transcribed Image Text:Problem 0.3 A = Consider a 2 x 2 matrix A and v, w€ R² 1 4 --- --- 2 (1) Find all eigenvectors of A. (2) Find [A]Â with respect to the ordered basis B = (v, w) (3) Give an explicit formula for An. ¹Think about what it means geometrically, in relation with the shearing map from problem 0.2
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