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(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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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).
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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