O Let A = [a] (i) aij ≥ 0, Mnxn with the following properties. (ii) a₁ + a2 +...+ain = 1 for 1 ≤i, j≤n. 1) show that A has an eigenvalue 1. 2) The absolute value of any eigenvalue of A is less than or equal to 1.
O Let A = [a] (i) aij ≥ 0, Mnxn with the following properties. (ii) a₁ + a2 +...+ain = 1 for 1 ≤i, j≤n. 1) show that A has an eigenvalue 1. 2) The absolute value of any eigenvalue of A is less than or equal to 1.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 8BEXP
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![(1) (a) Let A = [aij]
(i) aij ≥ 0,
(ii) a₁ + a2 +
Mnxn with the following properties.
+ain = 1
for 1 ≤i, j≤n.
1) show that A has an eigenvalue 1.
2) The absolute value of any eigenvalue of A is less than or equal to 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2397270-c13f-4cbc-8085-ef9e58d3496f%2Fe53fbf56-8689-4151-a570-6e6cbbf9b553%2Flkfyrbk_processed.png&w=3840&q=75)
Transcribed Image Text:(1) (a) Let A = [aij]
(i) aij ≥ 0,
(ii) a₁ + a2 +
Mnxn with the following properties.
+ain = 1
for 1 ≤i, j≤n.
1) show that A has an eigenvalue 1.
2) The absolute value of any eigenvalue of A is less than or equal to 1.
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