find all of the eigenvalues of the matrix A over the indicated p.
9/19: Chapter 4: 1. Existential statements can be proven by example 2. Universal statements cannot be proven by example 3. An integer n > 1 is prime if its only divisors are 1 and itself (known as trivial factors) 4. An integer n > 1 is composite if it is not prime a. Working definition – Integer n > 1 if there exists integers r and s such that 1 < r < n, and n = r * s 5. Proving existential statements [ x ∈ D, P(x)]: a. Need an example of an object x that comes from domain D and has property P (x must satisfy all properties of P) i. Leave no work to the reader b. Ex. 1: Prove that there exists distinct integers m and n such that (1/m) + (1/n) is an integer i. Do scratch work on a separate piece of paper ii. m = -2, n = 2 1. (1/-2) + (1/2) = 0 iii. Need to let the reader know the proof is starting (Pf// , Proof: , etc.) iv. Pf// Let m = (-2) and n = 2. Notice -2 and 2 are distinct integers. Further, (1/m) + (1/n) = (1/-2) + (1/2) = 0, which is an integer. 6. Proving universal statements [ x ∈ D, P(x)] a. We may not use an example in our proof proper; We must use variables to craft our argument. These variables represent objects from domains specified in the statement we wish to prove b. Ex. Prove that the sum of any two o