Sharp EL-W531X - Matrix Calculation: Matrix Powers

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Finding a
3
and b
3
in the same way,
After 5 years: C = A
5
= A
2
x A
3
(Refer to Example 2 - 1)
(Refer to Example 2 - 2)
Expressing the coefficients as a matrix gives
From the above, the coefficients of the calculation formula of each
company's share after 5 years can be found by repeated application of
matrix A.
: This is equal to matA
3
. (Refer to Example 1)
0.781 0.438
0.219 0.562
A
3
=
a
3
= 0.781a
0
+ 0.438b
0
b
3
= 0.219a
0
+ 0.562b
0
The shares of manufacturers A and B after 5 years and 10 years are
a
2
= 0.72269a
0
+ 0.55462b
0
= 57 %
b
2
= 0.27731a
0
+ 0.44538b
0
= 43 %
Matrix Calculation