Consider the matrix = [³9] 0 a where a E R is a real parameter. Which of the following statements is true? A a) A has two coincident eigenvalues if and only if a = 2 b) Det(A) = 0 for any a ER c) A homogeneous system having A as matrix of coefficients is consistent only if a 0 d) The eigenvalues of A are never coincident, Va E R e) Only one eigenvalue of A is a real number for a < 0

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the matrix
A
-
where a E R is a real parameter. Which of the following statements is true?
a) A has two coincident eigenvalues if and only if a = 2
b) Det(A) = 0 for any a ER
c) A homogeneous system having A as matrix of coefficients is consistent only if a # 0
d) The eigenvalues of A are never coincident, Va E R
e) Only one eigenvalue of A is a real number for a < 0
Transcribed Image Text:Consider the matrix A - where a E R is a real parameter. Which of the following statements is true? a) A has two coincident eigenvalues if and only if a = 2 b) Det(A) = 0 for any a ER c) A homogeneous system having A as matrix of coefficients is consistent only if a # 0 d) The eigenvalues of A are never coincident, Va E R e) Only one eigenvalue of A is a real number for a < 0
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