Let B 2 0 0 0 1 0 0 0 2 C 120 1 4 1 0 2 2 3 8 E 9 4 3 14

Let B = (2 0 0 0 -1 0 0 0 -2), C = 1/2(0 1 4 1 0 -2 2 3 8), E = (-9 -4 3 14 8 -4 -3 -2 1). Let A = CBE. Explain why A is invertible. Find A^11 (-2 0 6) explaining your work Let A be an m times n matrix and you are told that for a certain vector b espilon R^m the collection of the solutions of the equation Ax = b is the set S = {(1 2 3) + t (1 1 1) |t epsilon R}. Answer the following questions without explaining your answer. n = dim (N(A))) = rank (A) = Either find m or state that m is not determined by the given conditions.

Solution

6)

a) n=3

b) dim (N(A))=1

c) Rank A=2

d) m can be any number greater than 2