Hello everybody.

I'm having a little bit of trouble understanding a passage of my textbook regarding a linear transformation and matrix multiplication, I wonder if you could help me out.

So, I have this equation:

Where **F **is some 3x3 matrix and **x **a 3x1 array. For now, these are the important variables. So, my objective is putting **F** in a specific format called control canonical form (**A**), which is:

For that, the book shows a Linear Transformation in the variable x:

Which leads to (see first equation):

The equation for **A** is:

Where * T^{-1} *is defined as:

Writing everything in therms of * T^{-1} *:

Now, the problem:

I don't understant the right part of the equation. How can I multiply * T^{-1}*, which is a 3x1 array, with the 3x3

**F**matrix? Why the book shows a array with every single term of

*multiplying*

**T**^{-1 }**F**? I apologize if this is some stupid question but linear algebra isn't my strong suit.

Thanks!