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Screenshot of said problem:

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This is an exercise in an introduction to linear algebra course.

I'm having lots of trouble understanding how I should solve this question using matrices, or even how to form the equations initially. I don't think I even understand this question at all to be honest.

If this were something like compound interest, then I would know how to form an equation like $$\large x_{\text{no.of years}}=Ax_{\text{no.of years}-1},$$ where $A$ is the compound interest matrix and $x_{\text{no.of years}}$ is the amount of money in the account after whatever number of years.

Another example would be population changes across a few countries, such as 1/2 of people from country A migrating to B, and 1/2 from B to C, and 1/4 from C to A.

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Here are some notes of my thoughts about it, maybe it is not completely right, but I think it might give you an idea how this problem can be solved enter image description here