Consider the following matrices and vector: 12-4 2 -1 3 2 0 -4 A241 R= -3 50 1 2 10 3 (a) Compute the decomposition PA - LU (by hand!). Show the intermediary steps like we did in lecture 5/6 (b) Use the decomposition you found at (a) to solve Ax = R (by hand!) (c) Use Gaussian elimination to solve Bx - R (by hand!). Show intermediary steps like we did in lecture 5. (d) Compute the condition number of C (use Python/SciPy). If we solve Cr = Q, where Q is a 2-vector of which we know the entries up to 5 digits of precision, then how accurately can we compute