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.

 
 a)

3

 B)

one

 NS)

0

 D)

2nd

 TO)

4

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