Show that the product of the roots (real and complex) of the characteristic polynomial

Chapter 6, Problem 11

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QUESTION:

Show that the product of the roots (real and complex) of the characteristic polynomial of A is equal to det A. (Hint: If 1, . . . , n are the roots, show that p(t) = (t 1)(t 2) (t n).)

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QUESTION:

Show that the product of the roots (real and complex) of the characteristic polynomial of A is equal to det A. (Hint: If 1, . . . , n are the roots, show that p(t) = (t 1)(t 2) (t n).)

ANSWER:

Step 1 of 2

Show that determinant of a matrix equals the product of the roots of its characteristic polynomial.

Let  be the roots of the characteristic polynomial of .Then the characteristic polynomial can be written as

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