1. power of matrix

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.

2. Re: power of matrix

$\begin{pmatrix} 0.3 & 0.4 \\ 0.7 & 0.6 \end{pmatrix} \begin{pmatrix} 100 \\ 200 \end{pmatrix} = \begin{pmatrix} 110 \\ 190 \end{pmatrix}$

$\begin{pmatrix} 0.3 & 0.4 \\ 0.7 & 0.6 \end{pmatrix} \begin{pmatrix} 110 \\ 190 \end{pmatrix} = ?$

Finish that and do it again.

If you want higher powers you could diagonalize the matrix. Diagonalizable matrix - Wikipedia, the free encyclopedia

3. Re: power of matrix

I see...
A power of 2 =
109
191
correct?
Thank you.