(i 3) 2 2 (a) Let A = be a 2 x 2 matrix. (i) Compute det(A) and tr(A) (i.e., trace of A which is the sum of the main-diagonal entries). (ii) Is A invertible? Justify your claim. (Hint: Use the result from (i) above!) (iii) Compute the characteristic polynomial of A. (iv) Compute the eigenvalues of A. (v) Compute a basis for each eigenspace of A (i.e., corresponding eigenvector for each eigenvalue obtained in (iv)).

(i 3) 2 2 (a) Let A = be a 2 x 2 matrix. (i) Compute det(A) and tr(A) (i.e., trace of A which is the sum of the main-diagonal entries). (ii) Is A invertible? Justify your claim. (Hint: Use the result from (i) above!) (iii) Compute the characteristic polynomial of A. (iv) Compute the eigenvalues of A. (v) Compute a basis for each eigenspace of A (i.e., corresponding eigenvector for each eigenvalue obtained in (iv)).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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