3.43 Find the formula for the n-th power of this matrix.
Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P−1AP is the diagonal form of A. Prove that Ak = PBkP−1, where k is a positive integer. Use the result above to find the indicated power of A. A = −4 0 4 −3 −1 4 −6 0 6 , A5
Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that Ak = Pekp-1, where k is a positive integer. Use the result above to find the indicated power of A. 0-2 02-2 3 0 -3 ,45 A5 = 11
A is Complex matrix, sps, A is nor（）mal, and A to the power of k = 0 and k is greater than one Show A= 0;
Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = p-1AP is the diagonal form of A. Prove that A* = Pokp-1, where k is a positive integer. Use the result above to find the indicated power of A. 10 18 A = -6 -11 18].46 A = 11
[3] 2. Find the radius of convergence of the power series z" 5(n/2) n=1
Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = p-1AP is the diagonal form of A. Prove that Ak = pokp-1, where k is a positive integer. Use the result above to find the indicated power of A. -10 -18 A = 6 11 18].45 -253 -378 A6 = 126 188 11
Q [3] 2. Find the radius of convergence of the power series zn 5(n/2) n=1
Find the radius of convergence of the following power series: ю 3 zn 5(n/2) n=1
Write an algorithm that estimates the desired eigenvalues of an input matrix by using the power method. Your algorithm must find the i^th largest eigenvalues by using the power method and deflation to remove an already determined dominant eigenvalues. Save your algorithm as "LastnamePM.m." Your algorithm must be a function of A (input matrix), n (the number of iterations), and i (the i^th largest eigenvalues). For example, if you call "LastnamePM(A, 10,3)", the outcome will be the estimated 3,d largest...