Answer: Let A be an /1 x I! mntrix. (a) Show that del (A) is the product of all the
Chapter 7, Problem 24(choose chapter or problem)
Let A be an /1 x I! mntrix. (a) Show that del (A) is the product of all the roots of the character ~lic polynomial of A. (b) Show that A is singu lar if and only if 0 is an eigenvalue of A. (c) Also prove the analogous statement for a linear transformation: If L : V -+ V is a linear transformation. show that L is not oneto-one if and ooly if o is an eigenvalue of L. (d) Show Ihal if A is nilpotent (see Supplementary Exercise 22 in Chapter I). then A is singula
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