Consider the following 5 sentences about matrices. 2 of the statementsare 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).

Answered: Image /qna-images/answer/a07bd4b1-1dc8-4ad1-b6f8-d6bc1b28ea16.jpg

(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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section: Chapter Questions

Problem 1RQ

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