(1) If A is nx n, then A and A have the same eigenvalues. (ii) If A is nx n, then A and A have the same eigenvectors. (iii) If A is nx n then det(4*) = [det(4)]* (iv) If I is the n x n identity matrix, and J is an n xn matrix consisting entirely of ones, then the matrix I- is invertible and (I-1 = 1+J.
(1) If A is nx n, then A and A have the same eigenvalues. (ii) If A is nx n, then A and A have the same eigenvectors. (iii) If A is nx n then det(4*) = [det(4)]* (iv) If I is the n x n identity matrix, and J is an n xn matrix consisting entirely of ones, then the matrix I- is invertible and (I-1 = 1+J.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the following 5 sentences about matrices. 2 of the statements
are false in general. Figure out which 2 statements are false.
1) If A is nx n, then 4 and A have the same eigenvalues.
(i) If A is nx n, then A and A! have the same eigenvectors.
(ii) If A is nxn then det(4*) = [det(4)]*
(iv) If I is the nx n identity matrix, and J is an n xn matrix consisting entirely of ones,
then the matrix I-! is invertible and (I-)1 = 1+J.
(v) If I is the nxn identity matrix, and J is an nx n matrix consisting entirely of ones,
then the matrix A=I- is idempotent (i.e., A A).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb80f6022-58d7-401a-bedf-0dd897086f9b%2Fa07bd4b1-1dc8-4ad1-b6f8-d6bc1b28ea16%2Fk4zrbbs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following 5 sentences about matrices. 2 of the statements
are false in general. Figure out which 2 statements are false.
1) If A is nx n, then 4 and A have the same eigenvalues.
(i) If A is nx n, then A and A! have the same eigenvectors.
(ii) If A is nxn then det(4*) = [det(4)]*
(iv) If I is the nx n identity matrix, and J is an n xn matrix consisting entirely of ones,
then the matrix I-! is invertible and (I-)1 = 1+J.
(v) If I is the nxn identity matrix, and J is an nx n matrix consisting entirely of ones,
then the matrix A=I- is idempotent (i.e., A A).
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