Let Mn(a,b) be the n-by-n matrix, all of whose diagonal entries are equal to a and all of whose off-diagonal entries are equal to b. Find the eigenvalues of Mn(a,6), their algebraic and geometric multiplicities; and bases for the eigenspaces. (b) Find an invertible matrix P and a diagonal matrix D such that Mn(a,6) = PDP^(-1). (c) Use the result of (b) to find the determinant of Mn(a,b) and the characteristic polynomial of Mn(a,b).
Let Mn(a,b) be the n-by-n matrix, all of whose diagonal entries are equ…
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