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Chapter 7: Q24E (page 383)

TRUE OR FALSE

The determinant of a matrix is the product of its eigenvalues (over C), counted with their algebraic multiplicities.

Short Answer

Expert verified

The given statement is true

Step by step solution

01

Define eigenvalue

Eigenvalues are a set of specialized scales associated with a system of linear equations. The corresponding eigenvalue is often denoted by 位.

02

Explanation

This applies according to Theorem 7.5.5, 鈥淭race, determinant, and eigenvalues.鈥�

Consider an n x n matrix with complex eigenvalues 位 1, 位 2, 位 3 ,...., 位 nlisted with their algebraic multiplicities. Then

迟谤础=位 1+ 位 2+ 位 3 +....+ 位 n

And

诲别迟础=位 1位 2位 3 ... 位 n

According to the theorem the Statements is True

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[3-25107002]

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14.(100-500001)
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