1D State Vector and More Multiplication

Matrix Multiplication

Let's walk through that last quiz example, step-by-step.

Multiply the first row by the first column and sum.

Then, the second row, by the first column.

Then back to the first row, this time, multiplied by the second column.

And, finally the last step:

The last row multiplied by the last column.

To get our complete, resulting matrix!

Constant velocity

This kind of multiplication can be really useful, if x and y are not dependent on one another. That is, there is a separate and constant x-velocity and y-velocity component. For real-world, curved and continuous motion, we still use a state vector that is one column, so that we can handle any x-y dependencies. So, you'll often see state vector and transformation matrices that look like the following.

These extra spaces in the matrix allow for more detailed motion models and can account for a x and y dependence on one another (just think of the case of circular motion). So, state vectors are always column vectors.