Page 254 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

Unit matrix
(4 6) 14 1
A + B = B + A =
01 The matrix I = (1 0
=
Note that:
)is called a unit matrix, because it is a diagonal matrix with each leading
(4 6 ) 14 1
diagonal element equal to 1.
The unit matrix is denoted by the letter I and has
a magnitude of 1.
1 is the identity matrix for the multiplication of 2 x 2 matrices.
ADDITION AND SUBTRACTION OF MATRICES
Matrices can only be added or subtracted if they are of the same order.
) and B = (
The addition of matrices is commutative.
Let A = ( a b cd
)
I= ( 0 0 00
Then A + B =( a b cd
)+(
e f gh
) =(abef
e f gh
Let A = ( a b) c d
and
I = ( 0 0
0) 0
Then A + I =( a b cd
0 0 00
)+( =(a+0 b+0)
) c+0
d+0 =(a b
) So A + I = A.
cd
) is the identity matrix for the addition of 2 x 2 matrices.
EXAMPLE 2
Let A = (-5 7 06
=
( 7 + [-3] 9+ 5
-2 + 8 ) 1 + 0
cdgh
)
) and I = ( A + I
0 0 00
)
EXAMPLE 1
Find Now
( -5 7 ) + ( 0 0 ) 06 00
)
gh
B = ( e f )
If A = (7 -2 ) and B = (-3 8 ), find = (5+0 7+0 9150 +6+0
(a) A + B
(a) Now A + B
(a) Now A + B
(b) B + A
= (7 -2 )+ (-3 8 )
00
= ( -5 7 ) 06
= (-3
91
50
So A + I = A.
cd
Let A = ( a b ) and
=(a􏰁e b􏰁f) c􏰁g d􏰁h
gh (7 - 3 8 - 2 Then A + B =( a b ) 􏰁 ( e f
)
) =
=cd
(
)
14 1
4 6 14 1
8)+(7 -2 ) 5091
= (-3 + 7 5+ 9
8 - 2 0 + 1
=
248
A + I =