Using Python:
Background. The inverse of a square matrix, A, denoted as A^-1 is the matrix such that A A^-1 = I, where I is the identity matrix. One way to find A^-1 is using Gauss Elimination to solve the equation = where x is a square matrix
Background. The inverse of a square matrix, A, denoted as A is the matrix such that AA- is the identity matrix. One way to find A is using Gauss Elimination to solve the equation Ax x is a square matrix where I I where For example, given the matrix 3can find the inverse by using gauss elimination as follows r= 1 0 0.428 0.285 0 1 0.286-0.142 Reduce to get -3 0 1 The inverse is in the last two columns of the reduced matrix. Assignment. Write a function that returns the inverse of a square matrix. Your program should have the following structure def mylnverse(A): # create a copy of A # concatenate the identity matrix to the matrix # use gauss elimination to reduce the matrix-you don't need to implement pivoting # extract the inverse part (last n columns) of the reduced matrix # return the inverse A np.array([[1,21,[2,-3]) LAs mylnverse(A) print(iA) Useful numpy commands np.eye(n) creates an nxn identity matrix np.concatenate(A,B), axis-1) joins the matrices A and B B-Alam :n] B is a new matrix made of up columns, m to n-1, of A np.linalg.inv(A) returns the inverse of matrix A (you can use this command to check your result) Challenge. Implement pivoting in your gauss elimination code. You can test by finding the inverse of 1/3 0 1/3 A 2 12 A4/3-1-2/3 Background. The inverse of a square matrix, A, denoted as A is the matrix such that AA- is the identity matrix. One way to find A is using Gauss Elimination to solve the equation Ax x is a square matrix where I I where For example, given the matrix 3can find the inverse by using gauss elimination as follows r= 1 0 0.428 0.285 0 1 0.286-0.142 Reduce to get -3 0 1 The inverse is in the last two columns of the reduced matrix. Assignment. Write a function that returns the inverse of a square matrix. Your program should have the following structure def mylnverse(A): # create a copy of A # concatenate the identity matrix to the matrix # use gauss elimination to reduce the matrix-you don't need to implement pivoting # extract the inverse part (last n columns) of the reduced matrix # return the inverse A np.array([[1,21,[2,-3]) LAs mylnverse(A) print(iA) Useful numpy commands np.eye(n) creates an nxn identity matrix np.concatenate(A,B), axis-1) joins the matrices A and B B-Alam :n] B is a new matrix made of up columns, m to n-1, of A np.linalg.inv(A) returns the inverse of matrix A (you can use this command to check your result) Challenge. Implement pivoting in your gauss elimination code. You can test by finding the inverse of 1/3 0 1/3 A 2 12 A4/3-1-2/3
