Matrices are tools to solve linear equations. Engineers use matrices in solving electrical problems in circuits using Thevenin's and Norton's theories.
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false
Many real life physics problems are parabolic in nature. Parabolas can be shown as a quadratic equation. If you have two variables then usually you can use the equation to find the best solution to a problem. Also, it is a beginning in the world of mathematical optimization. Some equations use more than two variables and require the technique used to solve quadratics to solve them. I just ran an optimization of 128 variables. To understand the parameters I needed to set I had to understand quadratics.
Yes, it cannot contain any imaginary numbers
The dot-product and cross-product are used in high order physics and math when dealing with matrices or, for example, the properties of an electron (spin, orbit, etc.).
you don't.