FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.59Example
If A example of
a b
c d
=
then kA
ka kb
kc kd
=
Addition or subtraction of two matrices
The sum or difference of two matrices is defined only for the matrices of the same order. To add/subtract
two matrices we add/subtract their corresponding elements.
Example 101 :
2 3 4 1 3 2
5 6 7 1 6 8(^) +
(^) − (^)
3 6 6
4 12 15
=
Example 102 :
3 5 2 6
7 9 8 2(^) −
(^)
1 1
1 7
= −
−
Properties of matrix addition
♦ A + B = B + A (Commutative law)
♦ (A + B) + C = A + (B + C) (Associative law)
♦ k(A + B) = KA + KB (K is a Scalar)
♦ A + (–A) = (–A) + A = O
♦ A + O = O +A = A (O is null matrix)
SELF EXAMINATION QUESTIONS
(1) Evaluate
3 2 2 1 3
4 7 4 9 +
Ans.^58
12 25
(2) Evaluate
3 5 2 1 2 5 9
2 7 3 4 8 15 + −
Ans. 0 0
0 0