Construct a matrix C as follows. Set
A = round(100 * rand(4))
L = tril(A,-1) + eye(4)
C = L*Lʹ
The matrix C is a nice matrix in that it is a symmetric matrix with integer entries and its determinant is equal to 1. Use MATLAB to verify these claims. Why do we know ahead of time that the determinant will equal 1? In theory, the entries of the exact inverse should all be integers. Why? Explain. Does this happen computationally? Compute D = inv(C) and check its entries using format long. Compute C * D and compare it to eye(4).