In a certain elementary school, it has been found that of those pupils who buy a hot lunch on a particular school day, 30% buy a hot lunch and 70% bring a bag lunch on the next school day.
Furthermore, of those pupils who bring a bag lunch on a particular school day, 40% buy a hot lunch and 60% bring a bag lunch on the next school day.
Suppose that u1 = 100 pupils buy a hot lunch and u2 = 200 pupils bring a bag lunch on the ﬁrst day of school.
A power 2
and A power 3
I have a matrix A
.30 .40 100
.70 .60 200
1. Not sure how to reduced echalon on it. Do I change it to fractions first to make it easy to calculate?
3/10 4/10 100
7/10 6/10 200
2. Then A will be ?
1 0 200
0 1 100
3. how can I calculate A power of 2 and A power of 3?