Reddit reviews Mathematics for Economics - 2nd Edition

The only possible issue I see is your selection of textbook: Principles of Mathematical Economics - I've honestly never heard of this book.

The graduate school go-to textbook is Mathematics for Economists by Simon and Blume. However, I think this book would be overkill for you, as it is geared towards pure, PhD level, economics. Also, I was in a similar place to you, with respect to mathematical training at one point, and Simon & Blume proved to be too large a leap.

My advice would be to use one of the following books (in order of my preference):
1. Essential Mathematics for Economic Analysis by Sydsaeter
2. Mathematics for Economics
by Hoy
3. Fundamental Methods of Mathematical Economics
by Chiang

They'll bring your basic command, of the basic required mathematics up to scratch AND these books cover linear algebra. You will also then be in a good place to tackle Simon & Blume if you ever need to in the future. Another piece of advice: PRACTISE PRACTISE PRACTISE. For what you are doing, you don't need to have a deep understanding of the mathematics you are using BUT, you do need to be very comfortable with applying the techniques.

So, as you are working through (for instance) Sydsaeter, I would be attempting the related practice questions you find in:

1. Schaum's Outline of Calculus
   
2. Schaum's Outline of Linear Algebra
   
3. Schaum's Outline of Introduction to Mathematical Economics
   
   Hope this helps.
   
   P.S. Almost all of these books are available for 'free' on Library Gensis