2017-18 Google Drive (74) WhatsApp com/drive/folders/1UKOJAMO pey Let A = (03;] be an invertible diagonaal matrix,chais

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2017 18 Google Drive 74 Whatsapp Com Drive Folders 1ukojamo Pey Let A 03 Be An Invertible Diagonaal Matrix Chais 1 (287.67 KiB) Viewed 17 times

2017-18 Google Drive (74) WhatsApp com/drive/folders/1UKOJAMO pey Let A = (03;] be an invertible diagonaal matrix,chais B 1. Comptite the number of operations needed for solve the system by Gauss elimination (without partial pivoting) (3 marks) 3. V let 5811 18/14/20 120/80 Find a lower triangular matrix L with all the diagonal entries equal to 1 and an upper triangular matrix U such that ALU. Also find the determinant of A. (5 marks) Let D be a digonal matrix of size n with diagonal entries dina dan. Show that ||$||2 = max #max []dH:10 = 1. n}: (3 marks) 4. (a) Let qo, 91,--. be the orthonormal polynomials with respect to the usual inner product (69=1430(=/do obtained by applying Gram-Schmidt orthonormalization process to {1.1, 42,144.} Note that span{90, 91, n+1} = span{1,2 }Let Un+1(t) = Antica - 20)(2 4* H.) For i = 0,1,..., n, lct 16+) = IT (0) 240 PAL denote the Lagrange polynomial Show that 142) =* (1 mark) 1=0 1: (x)},{c)da = 0, (2 marks) iii. Llavero 1(a)do 01=0,1, (2 marks) b) Let 4 - ( 16 32