Question Given the matrices A=[} -1&1 1&1 ] solve for the matrix X in the equation XA+5B=C

To solve for the matrix X in the equation , we need to isolate X on one side of the equation.First, let's rewrite the equation as .Next, we need to find the inverse of matrix A, denoted as . The inverse of a matrix is a matrix that, when multiplied with the original matrix, results in the identity matrix.Once we have the inverse of matrix A, we can multiply both sides of the equation by to isolate X.So, .Now, let's calculate the inverse of matrix A: To find the inverse of a 2x2 matrix, we swap the diagonal elements and change the sign of the off-diagonal elements: Now, let's calculate : Finally, let's calculate : Therefore, the matrix X in the equation is .