I'm supposed to find a fundamental set of solutions of the system x' = [4, 0; 3, -1]x, and then using the fundamental set to compute the matrix exponential function e^(At). I have the fundamental solution, which is y(t) = e^(4t)[(5/3); 1] + e^(-t)[0;1] , but how the heck do I get the matrix exponential function e^(At)?

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I'm supposed to find a fundamental set of solutions of the system x' = [4, 0; 3, -1]x, and then using the fundamental set to compute the matrix exponential function e^(At). I have the fundamental solution, which is y(t) = e^(4t)[(5/3); 1] + e^(-t)[0;1] , but how the heck do I get the matrix exponential function e^(At)?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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