Solution Found!
Show that the product of the roots (real and complex) of the characteristic polynomial
Chapter 6, Problem 11(choose chapter or problem)
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).)
Questions & Answers
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