Given the matrix A below, find the three matrices that will diagonalize it into A = PDP-1. Use Mathematica to find the components of P and D, then to find P-1. Verify that your matrices multiply together to yield the original matrix A. 4 0 A = 6 9 15 4 2 3 -21 1 -2 -2 2 12 20 28 14 11 2 -4 10 10 -6 5

Let V, E, and F be the number of vertices, number of edges, and number of faces of a cube. Consider the following Pascal-like triangle, but we define each entry in the triangle, other than those on the boundary of the triangle, is obtained by the difference of two entries in the row above. For example, h² = E − h} and h² = h} – 1. Find the value of h. 1 1 1 1_hỉ h² 1 h² h F E h²/22 V 3 3 h² h²

the minimum and maximum numbers that can be represented in two’s complement in 6 bits?

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