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W.D. HenshawMath 6800: Solutions for Problem Set 41.Consider the Householder reflector,F=I-2uu*,u*u= 1.Determine the eigenvalues and eigenvectors, determinant, and singular values ofF.1
3.Write a Matlab function[W,R] = house(A)that computes an implicit representation of a fullor reduced QR factorization forA∈Cm×nwithm≥nusing Householder reflections. The outputvariables are a lower triangular matrixW∈Cm×nwhose columns are the Householder vectorsvk,and an upper triangular matrixR∈CRn×n.Also write a Matlab functionQ = formQ(W)that takes the matrixWfromhouseand generatesthe full matrixQ∈Cm×m.(a) Test your program on the Vandermonde matrix from problem set 3 withm= 5. CompareQandRfrom the Matlab function[Q,R]=qr(A)to the output fromhouseandformQ. PrintQandR