Which of the following is true for a square matrix A? I. The trace of the matrix is equal to the sum of the eigenvalues of the matrix. II. The constant term of the characteristic polynomial of the matrix is equal to the determinant of the matrix. III. If the matrix is of order 4x4, the leading number of the characteristic polynomial is positive. IV. The product of the eigenvalues of the matrix is equal to the determinant of the matrix.
Which of the following is true for a square matrix A? I. The trace of the matrix is equal to the sum of the eigenvalues of the matrix. II. The constant term of the characteristic polynomial of the matrix is equal to the determinant of the matrix. III. If the matrix is of order 4x4, the leading number of the characteristic polynomial is positive. IV. The product of the eigenvalues of the matrix is equal to the determinant of the matrix.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Which of the following is true for a square matrix A? I. The trace of the matrix is equal to the sum of the eigenvalues of the matrix. II. The constant term of the characteristic polynomial of the matrix is equal to the determinant of the matrix. III. If the matrix is of order 4x4, the leading number of the characteristic polynomial is positive. IV. The product of the eigenvalues of the matrix is equal to the determinant of the matrix. |
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