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Because many interesting things have a vector space structure, and many interesting problems can be formulated as a linear algebra problem. So if you study them in general, that knowledge can be applied to all of these different scenarios.
In your course, you will probably see examples involving geometry, systems of equations, differential equations, polynomials, and maybe even other things.
Basically, you are simply continuing your algebra courses from high school -- you're simply progressing beyond the boring case where you're only manipulating real or complex numbers.
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