4. Let a = 24, b = 105 and c = 594.
(a) Find the prime...
4. Let a = 24, b = 105 and c = 594.
(a) Find the prime factorization of a, b and c.
(b) Use (a) to calculate d(a), d(b) and d(c), where, for any
integer n, d(n) is the number of positive divisors of n;
(c) Use (a) to calculate σ(a), σ(b) and σ(c), where, for any
integer n, σ(n) is the sum of positive divisors of n;
(d) Give the list of positive divisors of a, b and c.
Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8,...
Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8, 10, 12}, and C
= {4, 5, 6, 7, 8, 9, 10}.
Determine the following sets:
i. (A ∩ B) − C
ii. (A − B) ⋃ (B − C)
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases...
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases
for R2, and
let A =
3
2
0
4
be the matrix for T: R2 ? R2 relative to B.
(a) Find the transition matrix P from B' to B. P =
(b) Use the matrices P and A to find [v]B and [T(v)]B, where
[v]B' = [1 ?5]T. [v]B = [T(v)]B =
(c) Find P?1 and A' (the matrix for T relative...