Hexadecimal to Octal to Binary Notation

Give a procedure for converting from the hexadecimal expansion of an integer to its octal expansion using binary notation as an intermediate step. keywords: notations

Ordered Pairs and Sets and Set Operations ( Complement, Union and Intersection )

1. a) Recall that ordered pairs must have the property that (x,y) = (u,v) if and only if x = u and y = v. Prove that {{x}, {x,y}} = {{u}, {u,v}} if and only if x = u and y = v. Therefore, although we know that (x,y) does not equal {x,y} , we can define the ordered pair (x,y) as the set {{x}, {x,y}}. b) Show by an ex ...continues

Sets and Set Operations

4. Let A = {a, {a}, {{a}}} B = {ø, {a}, {a, {a}}} C = {a} Be subsets of S = {ø, a, {a}, {{a}}, {a, {a}}}. Find a) A C b) B C’ c) A B d) ø B e) (B C) A f) A’ B g) {ø} B 5. Let A = {x | x is the name of a former president of the US} B = {Ada ...continues

Questions about ordered pairs, ordered triples, binary/unary operations, postfix notation

1. Recall that ordered pairs must have the property that (x,y) = (u,v) if and only if x = u and y = v. a) Prove that {{x}, {x,y}} = {{u}, {u,v}} if and only if x = u and y = v. Therefore, although we know that (x,y) does not equal {x,y} , we can define the ordered pair (x,y) as the set {{x}, {x,y}}. b) Show by an exa ...continues

Finding an Unknown Matrix Using an Inverse

Find a matrix A such that ┌ ┐ ┌ ┐ | 1 3 2 | | 7 1 3 | | 2 1 1 | A= | 1 0 3 | | 4 0 3 | | -1 -3 7 | └ ┘ └ ...continues

Products of Diagonal 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 ]

Size of the Product Matrix

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 find the size of those that are defined. a) AB b)BA c) AC d) CA e) BC f) CB keywords: multiplying, multiplication, matrices

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 : Using Inverses to find a Multiplying (Multiplier) Matrix

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