For whatever it's worth, PDF versions of the book are all over Scribd. I bought it (twice) but am actually working from a "stolen" PDF.
Here's a litmus test for whether you would like it. This is how Strang introduces Gaussian elimination:
The problem is to find the unknown values of u, v, and w, and we shall apply Gaussian elimination. (Gauss is recognized as the greatest of all mathematicians, but certainly not because of this invention, which probably took him ten minutes. Ironically, it is the most frequently used of all the ideas that bear his name.) The method starts by subtracting multiples of the first equation from the other equations. The goal is to eliminate u from the last two equations.
That colloquial aside is irrelevant and would drive readers who are gritting their teeth to begin with crazy. I love it. It reminds me of my favorite old math prof to whom Euler was a close personal friend. If you find such a style delightful, this is the book for you.
Strang's goal in this book seems to be to get you as excited about the subject as he is, and share how he really thinks about it, convention be damned. That's why it's Hippie Strang!
Correction: I take the last sentence back. I have "Standard Strang" instead (it was cheaper).