2. Consider the linear system / 3 1 2 / 21 | 6 3 4 | 22 | 3 1 5 ) ( 23 ) d) @)-(3) = 10 1 ( 3 (a) Solve (by hand) the system by finding the LU-factorization and then carrying out the two- step triangular solves. (b) Solve the problem numerically using the PA = LU factorization. In MATLAB use [L, U, p] = lu(A,"vector"). (c) From the vector p returned in part (b), how can the corresponding permutation matrix P be constructed in MATLAB? 2. Consider the linear system / 3 1 2 / 21 | 6 3 4 | 22 | 3 1 5 ) ( 23 ) d) @)-(3) = 10 1 ( 3 (a) Solve (by hand) the system by finding the LU-factorization and then carrying out the two- step triangular solves. (b) Solve the problem numerically using the PA = LU factorization. In MATLAB use [L, U, p] = lu(A,"vector"). (c) From the vector p returned in part (b), how can the corresponding permutation matrix P be constructed in MATLAB