This problem in geometry has been solved in no less than EIGHT ways
by a pair of students. How would you solve it? How many of their
solutions can you follow? How are they the same or different? Which
do you like best?
Follow hints using a little coordinate geometry, plane geometry and
trig to see how matrices are used to work on transformations of the
Given probabilities of taking paths in a graph from each node, use
matrix multiplication to find the probability of going from one
vertex to another in 2 stages, or 3, or 4 or even 100.
Square matrices of the same dimension can be added, subtracted and multiplied. You can also convert a matrix into a scalar by taking the determinant. You can also multiply or divide a matrix by a scalar. Perfect for a game of matrix countdown!