Matrices

The n × n matrix A = [aij] is called a diagonal matrix if aij = 0 when i ≠ j. show that the product of two n × n diagonal matrices is again a diagonal matrix. Give a simple rule for determining this product.

Matrices

show that [2 3 -1] is the inverse of [7 -8 5 ] [1 2 1] [ -4 5 -3 ] [-1 -1 3] [1 -1 1 ]

Matrices problem

let A be a 3 × 4 matrix. B be a 4 × 5 matrix, and C be a 4 × 4 matrix. Determine which of the following products are defined and fine the size of those that are defined. a) AB b)BA c) AC d) CA e) BC f) CB

Discrete mathamatics proofs: induction, inclusion/exclusion principle, Pascal's formula

1. Please prove the following using induction. n choose 0 = n choose n = 1 for all n greater or equal to 0 n choose k = n – 1 choose k – 1 plus n – 1 choose k for all 0 < k < n; n greater than or equal to 0 2. Please prove using the Inclusion and Exclusion Principle. Patrons of a local bookstore can sign up fo ...continues

Matrices

Find the matrix A such that ┌ ┐ ┌ ┐ | 1 3 | | 6 5 | A | | = | | | 2 4 | | 1 2 | ...continues

Fibonacci Sequence

let (f_k) be the Fibonacci sequence, show that: a) For every integer n>= 0, we have f_4(n+1) = 3f_4n+1 + 2f_4n b) Use a) in order to prove by induction that ∀n Є N, 3 | f_4n

Discrete mathematics: Boolean Product

Boolean Product. See attached file for full problem description.

Solve the system of congrunence

Solve the system: 2x ≡ 1 (mod 3) 3x ≡ 2 (mod 5) 5x ≡ 3 (mod 2)

Discrete Structures

1) If f is the mod-5 function, compute each of the following. a) f(17) b) f(48) c) f(169) 3) Convert (1011101)2 to base 16 (i.e., hex) 4) Find the sum of products expansion of this Boolean function F(x,y) that equals 1 if and only if x = 1. Note: one can write out the phrase “y complement” to represent the notation f ...continues

Show, how the given binary search algorithm executes in case of given key value.

Given algorithm looks for a value in a nondecreasing sequence and returns the index of the value if it is found or 0 if it is not found. Input: A sequence si, ...... ,sj (j >= i >= 1) sorted in nondecreasing order, a value key, i, and j Output: The output is an index k for which sk = key, or if key is not in the sequence, t ...continues