Interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points. The Vandermonde method is the most straight-forward method which may be used to find an interpolating polynomial. The substitution of the points into the desired polynomial yields a system of linear equations in the coefficients of the polynomial. Suppose we have 3 points and we want to fit a quadratic interpolating polynomial through these points, ro+r12+r222 We can find an interpolating polynomial that passes through 3 points (21, y), (12, y2), (X3, 43) by solving the following matrix system. ro+r121 + 3r2x;= y1 ro+r122 + 3r2x2 = y2 ro +r123 + 3r2x3 = y3 a) The coefficient matrix for this system is a Vandermonde matrix. Compute the determinant of the Vandermonde matrix. b) Suppose entries of x are (0, 1, 2), and entries of y are the last 3 digits of your student number (If last 3 digits are yly2y3, the first entry of vectory is yl, the second entry is y2, the third entry is y3). Solve the matrix system with Cramer's Rule and obtain the interpolating polynomial. Interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points. The Vandermonde method is the most straight-forward method which may be used to find an interpolating polynomial. The substitution of the points into the desired polynomial yields a system of linear equations in the coefficients of the polynomial. Suppose we have 3 points and we want to fit a quadratic interpolating polynomial through these points, ro+r12+r222 We can find an interpolating polynomial that passes through 3 points (21, y), (12, y2), (X3, 43) by solving the following matrix system. ro+r121 + 3r2x;= y1 ro+r122 + 3r2x2 = y2 ro +r123 + 3r2x3 = y3 a) The coefficient matrix for this system is a Vandermonde matrix. Compute the determinant of the Vandermonde matrix. b) Suppose entries of x are (0, 1, 2), and entries of y are the last 3 digits of your student number (If last 3 digits are yly2y3, the first entry of vectory is yl, the second entry is y2, the third entry is y3). Solve the matrix system with Cramer's Rule and obtain the interpolating polynomial