Problem 2 Consider the following is a simple system of equations 22:- 3r2 = 5 3r+5r2 = 6 There are many easy ways to solve this linear system, but most generally, we prefer to represent systems of m linear equations and n variables as Ar=D (1) where A is a mxn matrix, 2 is a vector of n variables, and b is a vector of m variables. For the example under consideration, m = 2 and n = 2, and the system of equations can easily be solved in the following manner, =A To compute the inverse of A, where the matrix is given by 221 099] then the inverse is defined as 1-1 11 412 1 02-219 A A = 021 422 413 = det A-2011) where the determinant of a 2 x 2 matrix is given by det A = 1022-12021 Write a program to solve systems of two equations and two variables (m=2, n = 2), such as the example above. The program should take as input a set of vectors that define each equations and return the solution vector. For example, the vector 2.-3.5 would the equation 2.11 - 3r2 = 5. Your program should define a separate function to compute the inverse of any 2 x 2 matrix and check that the determinant is not zero to avoid any divide-by-zero errors. Solve the following systems of equations: Linear system 1: 2 + = 2 where the inputs to your program for this system would be 1,1,2) and (0,1,1). Linear system 2: 2x - 3r2 = 5 3.: + Grz = 6 where the inputs to your program for this system would be 2.-3.5 and 3.4.6. Problem 2 Consider the following is a simple system of equations 22:- 3r2 = 5 3r+5r2 = 6 There are many easy ways to solve this linear system, but most generally, we prefer to represent systems of m linear equations and n variables as Ar=D (1) where A is a mxn matrix, 2 is a vector of n variables, and b is a vector of m variables. For the example under consideration, m = 2 and n = 2, and the system of equations can easily be solved in the following manner, =A To compute the inverse of A, where the matrix is given by 221 099] then the inverse is defined as 1-1 11 412 1 02-219 A A = 021 422 413 = det A-2011) where the determinant of a 2 x 2 matrix is given by det A = 1022-12021 Write a program to solve systems of two equations and two variables (m=2, n = 2), such as the example above. The program should take as input a set of vectors that define each equations and return the solution vector. For example, the vector 2.-3.5 would the equation 2.11 - 3r2 = 5. Your program should define a separate function to compute the inverse of any 2 x 2 matrix and check that the determinant is not zero to avoid any divide-by-zero errors. Solve the following systems of equations: Linear system 1: 2 + = 2 where the inputs to your program for this system would be 1,1,2) and (0,1,1). Linear system 2: 2x - 3r2 = 5 3.: + Grz = 6 where the inputs to your program for this system would be 2.-3.5 and 3.4.6