New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries
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In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulæ for their LU-decompositions and inverses. To prove the claimed results, we write all the identities to be proven in q-word and then use the celebrated Zeilberger algorithm to prove required q-identities. © 2020, Hacettepe University. All rights reserved.