I am solving a problem regarding newton's method. We are using this as the function: click to see function
Thus these are the Jacobian Matrix and the set up for Newton's Method: click here to see Jacobian and set up for Newton's Method
We are asked to get the inverse of the Jacobian using Gaussian Elimination and I know using Gaussian Elimination that would be JJ^-1 = I
My main question: is what is the identity matrix to use given that J is a matrix that has matrix elements? I'm thinking that if J is 2 x 2 and its matrix elements all have 2x2 sizes using the common 2x2 identity won't work. because an element of the matrix can never be a scalar since each element is 2x2.
or am I missing something?