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The eigenvalues are given by the characteristic equation (1-x)((1-x)^2-4)=0, which gives the values x=1, x=-1 and x=3 . These eigenvalues correspond to the eigenvectors (0, 1, 0), (1, -1, -1) and (1, -...

equation of a circle: (x - a)^2 + (y - b)^2 = r^2, where the circle has centre (a, b) and radius r.
Let's draw the diagram, where (x, y) is some point on the circle, which for ease we'll call P, and...

In terms of structure I think it's important to break down the question into manageable chunks. This can be explained in the introduction - from my experience it's usually best practice to write an introd...

Patrick Caulfield’s ‘Greece on the Ruins of Missolonghi (after Delacroix)’ is vibrant and magical. It is an interpretation of Delacroix’s ‘Greece on the ruins of Missolonghi’ which captures the s...

Use integration by parts, by setting u=x and cos(x)=dv/dx. The final result should be xsinx + cosx + c.