
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.

Re: power of matrix
$\displaystyle \begin{pmatrix} 0.3 & 0.4 \\ 0.7 & 0.6 \end{pmatrix} \begin{pmatrix} 100 \\ 200 \end{pmatrix} = \begin{pmatrix} 110 \\ 190 \end{pmatrix}$
$\displaystyle \begin{pmatrix} 0.3 & 0.4 \\ 0.7 & 0.6 \end{pmatrix} \begin{pmatrix} 110 \\ 190 \end{pmatrix} = ?$
Finish that and do it again.
If you want higher powers you could diagonalize the matrix. Diagonalizable matrix  Wikipedia, the free encyclopedia

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