Show that the set below forms a group with matrix multiplication as the binary operation 10 {b} } [ 6 q]} 01 1 0 0 -

Find an LU-factorization of A = [ 21 -41

Write the permutation corresponding to R90 in the left regular representationof D4 in cycle form.

let a = 3^4 7^3 11^2 13^5 and b = 2^6 5^2 7^2 11^3 13^4 Determine the values of (a,b) and [a,b] and Find eight consecutive composite integers

Define the binary operator by: a + b = a + 2b Simplify each of the following. Do the order of operations (do what is in parentheses first). a. (45) 2 b. (3 + 7) + 6 = *

what is the element a34

20. Find the multiplicative inverse of the given element. (See example 4 of Section 2.6.) [Type here] [Type here] in in in in

Let [ a ] be an element of n that has a multiplicative inverse [ a ]1 in n. Prove that [ x ]=[ a ]1[ b ] is the unique solution in n to the equation [ a ][ x ]=[ b ].

Show that the system consisting of all elements of the form a+b√5, where a and b are any rational numbers, satisfies all the axioms for a field if the usual rules for addition and multiplication are used.