Linear algebra , Matlab code, overleaf editor, QR_Factorization

In the mathematical discipline of linear algebra, a matrix decomposition is a factorization of a matrix into a product of simpler matrices with nicer properties than the original matrix. There are many different matrix decompositions; each finds use among a particular class of problems. The video you had watched by Prof. Gilbert Strang from MIT motivates the study of this concept. In linear algebra, a QR-decomposition is a decomposition of a matrix A of size m × n into a product A = QR of an orthogonal m × n matrix Q and an upper triangular n × n matrix R. Recall that a matrix Q is orthogonal if its columns are orthonormal, meaning that Qt Q = Q Qt = I. There are several methods for computing the QR-decomposition, such as by means of Gram-Schmidt process, Househodler transformations, or Givens rotations. Please type your answers of the following exercises using LATEX through Overleaf