Question

3. Let A(alpha)= (as shown in picture)

a) Show that A(alpha)A(beta) = A(alpha+beta)

b) Use part (a) to find the Inverse if A(alpha)

4. Find the inverse (if they exist) of:

a). | 1 3|

| 2 4|

b) | 1 0 1|

| 2 -1 1|

| 1 2 1 |

c) [ 2 2i 0]

[ 2i -2 2+2i] , where i= (sqrt) of -1

[ 2-2i 0 4]

1 a III Let 4la) =0 1 0 0 a) Show that a).ap)la p) b) Use part (a) to find the inverse of 4la) IV Find the inverses (if they exist) of 31 a) 2 4 1 b) 2 -1 1 1 2 1 2 2 21 -2 2+28 where -1 2- 2 0 4 - -

Answer 1

(D Let ACaet) Then 3X3 - - y --) an d So from patC ACACD) (B ) ACC)AC-0)

FSinilany AL-A)A()2 So inverse of Ai A() (-072 a 1 1 -a Ca) 2 --2 10, co A exits 141 det A 4- ~21丁 A 2 (cay) -1 1 2 2 1 IC--2)-o+IC1) > 21 048 existe det B - 35

R 4 R3) - 2-1 4 2 -! 2 3 -2 1 -2P (Au) 1 - 2 21 2 -2 2+2 4 2-2i Iet afenjuan +2 + 4 -16 161 -2 -16+1G 2 1 N

-& -& i -641a) 4t41 +10i c's 191+1プ1 4-81 4-4 441 4441 -& -6 -0ti) X -4-41 2X/0 4-4i C