Find the sum and product of each of these pairs of num- bers. express your answers as a base 3 expansion. a.(112) 3 , (210) 3 b.(2112) 3 , (12021) 3 c.(20001) 3 , (1111) 3 d.(120021) 3 , (2002) 3

Adding in base 3 is very much like adding in base 10, but instead of carrying digits when their sum exceeds 9, we have to watch for when the sum exceeds 2:

.   112
+  210
- - - - -
.   322 -> 1022

.   12021
+    2122
- - - - - - -
.   14143 -> 14150 -> 14220 -> 21220

.   20001
+    1111
- - - - - - -
.   21112

.   120021
+      2002
- - - - - - - -
.    122023 -> 122030 -> 122100

Multiply on the left side with the following elimination matrix :

Multiply on the left by another elimination matrix :

Multiply on the left by the inverse of :

We have