Mathematics · Linear Algebra
Let M be a 7×7 matrix with real entries having the characteristic polynomial cM(x) = (x - 1)α(x - 2)β(x - 3)2, where α > β. Let rank(M - I7) = rank(M - 2I7) = rank(M - 3I7) = 5, where I7 is the 7×7 identity matrix. If mM(x) is the minimal polynomial of M, then the value of mM(5) is:
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