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

Show that A8 contains an element of order 15.

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

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

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.

Write each of the following permutations as a product of disjoint cycles. (a)  (1235)(413) (b)  (13256)(23)(46512) (c)  (12)(13)(23)(142)

10 a.) Completely simplify ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r + x-1)³ and simplify.

Consider the following group of numbers. 3 -7, v9, 16 5, 3.14159265. , 0, V14, 6 List the real numbers. (Enter your answers as a comma-separated list. Round your answers to eight decimal places as needed.)