4. By hand, compute the ALU decomposition of the following 4 x 4 matrix A 1-2-2-3]...

 

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4. By hand, compute the ALU decomposition of the following 4 x 4 matrix A 1-2-2-3] 3 -9 -95 -1 2 4 7 -3 -6 24 3 Be sure to include your working for each step of the procedure, including the forms of the L matrices and their respective inverses. 5. Write a Python function lu (A) which computes the LU decomposition in place without pivoting using Doolittle's method. Verify your routine by using it to compute the LU decomposition of the 4 x 4 matrix in Question 4. Hint: When implementing your routine recall that NumPy arrays are zero indexed. 6. Extend your LU decomposition routine to incorporate support for partial pivoting. Here, the function lu_pp (A) should compute the decomposition of A in-place and return the pivot matrix. 4. By hand, compute the ALU decomposition of the following 4 x 4 matrix A 1-2-2-3] 3 -9 -95 -1 2 4 7 -3 -6 24 3 Be sure to include your working for each step of the procedure, including the forms of the L matrices and their respective inverses. 5. Write a Python function lu (A) which computes the LU decomposition in place without pivoting using Doolittle's method. Verify your routine by using it to compute the LU decomposition of the 4 x 4 matrix in Question 4. Hint: When implementing your routine recall that NumPy arrays are zero indexed. 6. Extend your LU decomposition routine to incorporate support for partial pivoting. Here, the function lu_pp (A) should compute the decomposition of A in-place and return the pivot matrix.