n Exercises 9- 20. a linear operator T on R " and its clwracterisric polynomial are given. Find, if possible, a basis for R" consisTing of eigemecrors ofT. If no such basis exists. explain 20 T

Math 115 Textbook Notes: Chapter P the Fundamental Concepts of Algebra 1 Exponential Notation: b = b · b · b ·… ·b (Factors of n) Set: {1, 2, 3, 4, 5,} Union of Set: A U B = A or B Intersection of Set: A Ƞ B = A and B Subsets of the Real Numbers Name Description Examples Natural The # that we use for counting 2, 3, 5, 17 # Whole # Whole #’s that includes 0 and natural # 0, 2, 3, 5, 17 Integers Includes the negatives of the natural # and whole # -17, -5, -3, -2, 0, 2, 3, 5, 17 Rational All #s that can be expressed as a quotient of two -17=-17/1, 5= 5/1, 2/5=0.4, # integers