Extra task – NLAA– Numerical Linear Algebra with ApplicationsInstructions: Please upload to Canvas by the end of the Friday lecture in week 8 (March 8) asingle file corresponding to part (b) of the task below. Please name your file as suggested inthe question.Plagiarism check: Your electronic submissions should be your own work and should not beidentical or similar to other submissions. A check for plagiarism will be performed on all submissions.Let A ∈ Rn×m have full rank and let b ∈ Rn. Consider the least squares problem: find the minimiserx ∈ Rm of the functional F : Rm → [0,∞) given byF(x) := kb Axk2.(a) Modify the algorithm for the LU-factorization with partial pivoting so that it constructs thefactorizationP A = LU, (1)where P is a permutation matrix, U ∈ Rn×nis upper triangular and L代写Linear Algebra作业、代做Canvas留学生作业、代做matlab编程语言作业、代写matlab实验作业 ∈ Rm×nis unit lowertriangular (i.e., for 1 ≤ i ≤ n, Lij = 0 if j > i and Lii = 1). Write a function file luppgen.mwith A as input, while your output should be the factors LE, UE in the economy (thin) versionof (1) and a permutation vector corresponding to P.(b) Using the factorisation from part (a), derive the LU factorisation method for the least squaresproblem. Write a function file lslusolve.m to implement this method. Your input should beA, b, while your output should be the solution vector x. Your file should contain luppgen.mas a subfunction.Note: You should submit the matlab file for this task only if you are registered on the LM versionof this course (module code 27689), i.e., if you are a Year 4 or MSc student, or you registeredspecifically on the LM version as an exchange or Erasmus student.转自：http://www.3daixie.com/contents/11/3444.html