I rewrote q(x,y) in matrix notation, and I found the matrix A representing the quadratic form. I also rewrote the linear substitution using matrix notation, and I found matrix P corresponding to the substitution. And finally, I found q(s,t) of q(x,y) using direct substitution matrix notation. This is problem 12.35 from chapter 12 contained within the book "Linear Algebra, Schuam's Outline," (2018, S. Lipschutz, M. Lipson, McGraw-Hill Education) that aligns with linear algebra, advanced linear algebra, advanced physics, advanced engineering, and quantitative analysis.

I spent 3.5 years in a library reading and solving math problems contained within several math textbooks, such as intro. to elem. linear algebra w/ applications, discrete mathematics with applications, linear algebra; applications version by Anton and Rorres, while also studying two linear algebra textbooks I bought at Barnes and Noble with more advanced treatments that include problems that are in many graduate school classes.

My first exposure to linear algebra came from a class I was required to take for my major, BSEE at George Mason University, Fairfax, where we used the textbook with the title, Introduction to Elementary Linear Algebra with Applications required for all students in engineering majors - to graduate.

I completed a more advanced treatment of linear algebra textbook, Linear Algebra; Schaum's Outline that covers diagonalization, bilinear forms, quadratic forms, Hermitian forms, and more. I recently bought three advanced math textbooks (graduate/professional level-linear algebra and it's applications, theoretical linear algebra, and ordinary differential equations that cover quantum physics, applications in advanced engineering, such as ladder networks, Markov chains, minimal polynomial test problems, and a lot more.

-Mark R. Rowe

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