Question 1 (40 points) Compute the LU decomposition of the following matrix by hand by setting…

Question 1 (40 points) Compute the LU decomposition of the following matrix by hand by setting the diagonal entries of the matrix L to 1. Make sure to show as many steps are possible. 8 5) 10 5 2 6 Question 2 The following three parts are programming questions. If you check your work by computing the matrix products, the result may be a little bit off (less than le-10) from the original matrix due to computational limitations and thus is acceptable. Feel free to use popular packages (i.e. numpy and scipy for python pro- grammers). Please submit the code for each solution separately with the title firstName_lastName_Q2_P. Consider the following matrix for the following 3 parts: 10 -7 0 3 5 -1 5 Question 2.1 (20 points) Compute the LU decomposition of the matrix above and write down your solution. It is possible that you obtain a permutation matrix, P, from the result; if so, include it in your answer. Question 2.2 (15 points) Compute the SVD of the matrix above and write down the singular values. Question 2.3 (15 points) Compute the QR decomposition and write down the Q and R matrices. 8 10 5 10 -7 0 -3 2 6 6 -1 5

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