Please answer all questions

(1 point) Consider the following two systems. (a) -2x + 4y -3x - 5y -1 (b) -2x + 4y = -3x - 5y = 2 () Find the inverse of the (common) coefficient matrix of the two systems. A = (ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating AB where B represents the right hand side (l.e. B = for system (a) and B = for system (b)). Solution to system (a): x = Solution to system (b): x =(1 point) A square matrix is called a permutation matrix if it contains the entry 1 exactly once in each row and in each column, with all other entries being 0. All permutation matrices are invertible. Find the inverse of the following permutation matrix 0 0 1 07 0 0 A = 1 0 0 0 0 1 0 0 A- =(1 point) Find the LU factorization of A = 12 and use it to solve the system 3 X1 -11 -3 12 X2 -42 A = E X2-4 -3 ON (1 point) Find the LU factorization of A = -12 -12 16 0 and use it to solve the system -4 -3 2 -12 -12 6 16 0 -4 A = X2 X=(1 point) Solve for X. Assume X is a 2 x 2 matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated. : $1 * + 183 3 ]=13 - X. X =(1 point) The 2 x 2 elementary matrix E can be obtained from the identity matrix using the row operation r - r, + 4r2 . Find EA if -3 4 A = 3 -5 EA =