Mathematics 9 (Complete Solutions)

Q4
Perform the indicated operations and simplify the following.

(i)
 
1 0
0 1
 
+
 
0 2
3 0
 
+
 
1 1
1 0
 
(ii)
 
1 0
0 1
 
+
 
0 2
3 0
 
-
 
1 1
1 0
 
(iii)
 
2 3 1
 
+ (
 
1 0 2
 
-
 
2 2 2
 
)
(iv)
 
1 2 3
-1 -1 -1
0 1 2
 
+
 
1 1 1
2 2 2
3 3 3
 
(v)
 
1 2 3
2 3 1
3 1 2
 
+
 
1 0 -2
-2 -1 0
0 2 -1
 
(vi)
 
1 2
0 1
 
+
 
2 1
1 0
 
+
 
1 1
1 1
 


Solution:


(i)
 
1 0
0 1
 
+
 
0 2
3 0
 
+
 
1 1
1 0
 
=
 
1+0 0+2
0+3 1+0
 
+
 
1 1
1 0
 
=
 
1 2
3 1
 
+
 
1 1
1 0
 
=
 
1+1 2+1
3+1 1+0
 
=
 
2 3
4 1
 


(ii)
 
1 0
0 1
 
+
 
0 2
3 0
 
-
 
1 1
1 0
 
=
 
1+0 0+2
0+3 1+0
 
-
 
1 1
1 0
 
=
 
1 2
3 1
 
-
 
1 1
1 0
 
=
 
1-1 2-1
3-1 1-0
 
=
 
0 1
2 1
 


(iii)
 
2 3 1
 
+ (
 
1 0 2
 
-
 
2 2 2
 
)
=
 
2 3 1
 
+
 
1-2 0-2 2-2
 
=
 
2 3 1
 
+
 
-1 -2 0
 
=
 
2-1 3-2 1+0
 
=
 
1 1 1
 


(iv)
 
1 2 3
-1 -1 -1
0 1 2
 
+
 
1 1 1
2 2 2
3 3 3
 
=
 
1+1 2+1 3+1
-1+2 -1+2 -1+2
0+3 1+3 2+3
 
=
 
2 3 4
1 1 1
3 4 5
 


(v)
 
1 2 3
2 3 1
3 1 2
 
+
 
1 0 -2
-2 -1 0
0 2 -1
 
=
 
1+1 2+0 3-2
2-2 3-1 1+0
3+0 1+2 2-1
 
=
 
2 2 1
0 2 1
3 3 1
 


(vi)
 
1 2
0 1
 
+
 
2 1
1 0
 
+
 
1 1
1 1
 
=
 
1+2 2+1
0+1 1+0
 
+
 
1 1
1 1
 
=
 
3 3
1 1
 
+
 
1 1
1 1
 
=
 
3+1 3+1
1+1 1+1
 
=
 
4 4
2 2
 

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