Mathematics 9 (Complete Solutions)

Q6
Find

If
A =
 
1 -2
3 4
 
and
B =
 
0 7
-3 8
 
, find.

(i) 3A - 2B
(ii) 2At - 3Bt

Solution:

(i) 3A - 2B
= 3
 
1 -2
3 4
 
-
2
 
0 7
-3 8
 
=
 
3(1) 3(-2)
3(3) 3(4)
 
-
 
2(0) 2(7)
2(-3) 2(8)
 
=
 
3 -6
9 12
 
-
 
0 14
-6 16
 
=
 
3-0 -6-14
9+6 12-16
 
=
 
3 -20
15 -4
 



(ii) 2At - 3Bt
First we wil find At and Bt
A =
 
1 -2
3 4
 
At =
 
1 3
-2 4
 
B =
 
0 7
-3 8
 
Bt =
 
0 -3
7 8
 
Now by putting the value of At and Bt
= 2
 
1 3
-2 4
 
-
3
 
0 -3
7 8
 
=
 
2(1) 2(3)
2(-2) 2(4)
 
-
 
3(0) 3(-3)
3(7) 3(8)
 
=
 
2 6
-4 8
 
-
 
0 -9
21 24
 
=
 
2-0 6+9
-4-21 8-24
 
=
 
2 15
-25 -16
 

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