I teach these as separate subjects but I've often wondered if there is a connection of any sort. It appears that vectors are classified as matrix but matrix are not vectors.
I discovered this cool website which talks about using both vectors and matrices in real life with great examples and which math class it applies to.
So under Geometry, there are 10 different topics covered that use either vectors, matrix or both. For instance, in animation, it shows how vectors are used to determine how the light is shown on the figure composed of triangles. How to create 3 dimensional figures out of flat two dimensional painting. Or even bathroom tiled floors and getting it right.
Then there is physics and biology with a lovely exercise on modeling the climate change and melting of ice in the arctic. What about using vectors to model turbulence? That's included in 6 topics in this section.
What about game theory and computer science? Under this group, you can find game theory and soccer, or simple computer models to recreate the world. This talks about modeling gas molecules, flocks of birds, or even bats!
At the very end are 10 activities from the NRICH site to learn more about matrix and vectors. One activity has students figure out the shortest air route between London and Cape Town. Another students calculate the actual speed and bearing of an aircraft that is flying with a wind.
I especially love the piece on maths in computer modeling because it provides some very indepth information on this topic. It connects vectors to computer games and shows how it works. In addition, it has exercises for the student to play with. This article even gets down to explaining why triangles are used to form 3 dimensional objects and the job vectors do within simulations and other types of games. The information in this activity could easily be used for a full week in class.
Finally, there is a short article on what computers cannot do. There are limits that most of us don't worry about but the limits came out of code-breaking in World War II and the enigma machine. I think this would be a cool way to connect history with math so students see that each is not an isolated subject but interrelated.
Have fun exploring this site.