Question: solve this linear algebra questions a) Consider the following sequence S : 0,1,21,43,85, i. Find a matrix A that satisfies [Fk+2Fk+1]=A[Fk+1Fk] where Fk denotes the

solve this linear algebra questions

a) Consider the following sequence S : 0,1,21,43,85, i. Find a matrix A that satisfies [Fk+2Fk+1]=A[Fk+1Fk] where Fk denotes the kth term of the above-mentioned sequence S. ii. Diagonalize the matrix A so that you can easily produce the Ak for any number k. You do not need to multiply the decomposed elements to get a single matrix. iii. Find the 100th term of the sequence S. b) Is it possible to choose all of the eigenvectors of a real symmetric matrix perpendicular to each other? Justify your answer. a) Consider the following sequence S : 0,1,21,43,85, i. Find a matrix A that satisfies [Fk+2Fk+1]=A[Fk+1Fk] where Fk denotes the kth term of the above-mentioned sequence S. ii. Diagonalize the matrix A so that you can easily produce the Ak for any number k. You do not need to multiply the decomposed elements to get a single matrix. iii. Find the 100th term of the sequence S. b) Is it possible to choose all of the eigenvectors of a real symmetric matrix perpendicular to each other? Justify your

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