When a matrix A is square with full rank, there is a vector x that satisfies the equation Ax=b for any b. However, when A is not square or does not have full rank, such an x may not exist, because b does not lie in the range of A. In this case, called the least squares problem, we seek the vector x that minimizes the length (or norm) of the residual vector r=Ax-b. The four vectors Ax, b, r, and rmin are color coded and the plane is the range of the matrix A. The plane shown is the set of all possible vectors AxComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática