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.

Compute A

u1

u2

A power 2

u1

u2

and A power 3

u1

u2

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?

Thank you.