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Question: b1 consider the matrix i determine the two eigenvalues ...

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B1. Consider the matrix (i) Determine the two eigenvalues λ 1,2 of G and the normalised eigenvectors. Are the eigenvectors orthogonal to each other? () Consider the matrix F given by and compute the product F.G. Show that F is the inverse of G, F G1, provided that a 1,b-1,c 1 and d 0 (ii) Find the eigenvalues of the matrix G-1. Show by explicit computation or oth erwise that the eigenvalues of G1 are the inverse of the eigenvalues of G. [4] (iv) Show that G is not an orthogonal matrix. Hint: Compute the matrix G.

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