the matrix

(a) Show that the matrix 3 4 A-9 is diagonalisable over R. Hence find an invertible matrix M such that M-AM = D, where D is a diagonal matrix. (To gain full marks, you need to compute M-1 and check that indeed M-IAM = D.) (b) Solve the following system of first order differential equations using the results of item (a) above: dx = 3x + 4y, dt dy dt 2x + y
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