Basics of MATLAB and Beyond

Where p i is the population for year x i , and i =1, 2,...N. We can writethis series of equations as a matrix equation:⎛ ⎞ ⎛⎞p 1 1 x 1 x 2 1 ⎛p 2⎜ .⎝⎟. ⎠ = 1 x 2 x 2 2⎜⎝⎟ ⎝ c ⎞0c 1⎠ .. ⎠c 2p N 1 x N x 2 NOr, defining matrices,P = X · C .In matlab the X matrix is calculated as follows:>> X = [ones(size(year)) year year.^2]X =1 1788 31969441 1790 3204100...1 1993 39720491 1994 39760361 1995 3980025The backslash operator solves the equation for the coefficient matrix C:>> C = X\PC =1.0e+09 *2.0067-0.00220.0000The third coefficient is not really zero; it is simply too small (comparedto 2.0 × 10 9 ) to show in the default output format. We can change thisby typing:>> format long e>> CC =2.006702229622023e+09-2.201930087288049e+066.039665477603122e+02The backslash operator does its best to solve a system of linear equationsusing Gaussian elimination or least-squares algorithms, depending onwhether the system is exact, or over- or under-determined. We canc○ 2000 by CRC Press LLC