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 for advance notification of new book arrivals in genres of interest. In the first month of this service, 32 sign up for mysteries, 34 for spy novels, 18 for westerns, and 41 for science fiction. Of these, 17 sign for both mysteries and spy novels, 8 for both mysteries and westerns, 19 for mysteries and science fiction, 5 for spy novels and westerns, 20 for spy novels ... click for more

Matrices

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