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The first eigenvalue is 3, whose corresponding eigenvector is (1, 1), and the second eigenvalue is 2, whose corresponding eigenvector is (3, 4). In diagonal form, A = PDP^-1, where P = [[1, 3], [1, 4]] an...

In order to find the equation of the tangent to a curve at a point (x₁, y₁), we use the equation y - y₁ = m(x - x₁), where m is the gradient of the curve at (x<...

Unity just means 1, so we need to find all z such that z³=1. However, although we can immediately see that z=1 is a solution, when dealing with complex numbers some solution may not lie on the ...

Using the auxiliary equation t^2 - 2t - 3t = 0  t therefore is equal to 3 or -1. Using this value, a complementary function is derived.  Y= Ae^(3x) + Be^(-x). Finally, to fully solve, a particular integra...