Mathematics 9 (Complete Solutions)

Q3
Find

If
A =
 
-1 2
2 1
 
,
B =
 
1
-1
 
,
C =
 
1 -1 2
 
,
D =
 
1 2 3
-1 0 2
 
, then find ,

(i) A +
 
1 1
1 1
 
(ii) B +
 
-2
3
 
(iii) C +
 
-2 1 3
 
(iv) D +
 
0 1 0
-2 0 1
 
(v) 2A
(vi) (-1)B
(vii) (-2)C
(viii) 3D
(ix) 3C



Solution:



(i) A +
 
1 1
1 1
 

Putting A =
 
-1 2
2 1
 

=
 
-1 2
2 1
 
+
 
1 1
1 1
 

=
 
-1+1 2+1
2+1 1+1
 

=
 
0 3
3 2
 



(ii) B +
 
-2
3
 

Putting B =
 
1
-1
 

=
 
1
-1
 
+
 
-2
3
 

=
 
1-2
-1+3
 

=
 
-1
2
 



(iii) C +
 
-2 1 3
 

Putting C =
 
1 -1 2
 

=
 
1 -1 2
 
+
 
-2 1 3
 

=
 
1-2 -1+1 2+3
 

=
 
-1 0 5
 



(iv) D +
 
0 1 0
2 0 1
 

Putting D =
 
1 2 3
-1 0 2
 

=
 
1 2 3
-1 0 2
 
+
 
0 1 0
2 0 1
 

=
 
1+0 2+1 3+0
-1+2 0+0 2+1
 

=
 
1 3 3
1 0 3
 



(v) 2A

Putting A =
 
-1 2
2 1
 

= 2
 
-1 2
2 1
 

=
 
2(-1) 2(2)
2(2) 2(1)
 

=
 
-2 4
4 2
 



(vi) (-1)B

Putting B =
 
1
-1
 

= -1
 
1
-1
 

=
 
-1(1)
-1(-1)
 

=
 
-1
1
 



(vii) (-2)C

Putting C =
 
1 -1 2
 

= -2
 
1 -1 2
 

=
 
-2(1) -2(-1) -2(2)
 

=
 
-2 2 -4
 



(viii) 3D

Putting D =
 
1 2 3
-1 0 2
 

= 3
 
1 2 3
-1 0 2
 

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

=
 
3 6 9
-3 0 6
 



(ix) 3C

Putting C =
 
1 -1 2
 

= 3
 
1 -1 2
 

=
 
3(1) 3(-1) 3(2)
 

=
 
3 -3 6
 

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