subject- advanced linear algebra

pleasa solve it step by step

*7. Let A be the given matrix and U=En1Pn1En2Pn2E2P2E1P1A is an upper triangular matrix obtained from A using Gaussian elimination method with partial pivoting. Here, Pi and Ei are permutation and lower triangular matrices, respectively, for i=1,2,,n1. 1 (i). Prove that Pn1En2Pn1 is a lower triangular matrix. (ii). Let a matrix Mk=(Pn1Pn2Pk+1)Ek(Pk+1Pk+2Pn1), for k=1,2,,n2. Prove that each Mk is a lower triangular matrix. *7. Let A be the given matrix and U=En1Pn1En2Pn2E2P2E1P1A is an upper triangular matrix obtained from A using Gaussian elimination method with partial pivoting. Here, Pi and Ei are permutation and lower triangular matrices, respectively, for i=1,2,,n1. 1 (i). Prove that Pn1En2Pn1 is a lower triangular matrix. (ii). Let a matrix Mk=(Pn1Pn2Pk+1)Ek(Pk+1Pk+2Pn1), for k=1,2,,n2. Prove that each Mk is a lower triangular matrix