4. Three observations of a function y = f(x) were taken at points 11, 12, 13 (all r; are different): y1 = f(+1), y2 = f(

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4 Three Observations Of A Function Y F X Were Taken At Points 11 12 13 All R Are Different Y1 F 1 Y2 F 1 (38.66 KiB) Viewed 32 times

4. Three observations of a function y = f(x) were taken at points 11, 12, 13 (all r; are different): y1 = f(+1), y2 = f(x2), y3 = f(13). The function was interpolated by a polynomial regression of second order: f(x) = 40 +223 +22x². (a) Write down the system of equations for unknown parameters (0,01, 02. (b) Prove that this system always have a single solution. (Hint: you may use properties of So-called "Vandermonde" matrix - google it). (c) Given that 01 = 1, 12 = 2, 13 = 3, y1 = 4, y2 = 6, y3 = 6, find the parameters di. (d) Suppose another observation was added: y = f(x4). Suggest such values for 24 and y4 that the system for a; will: (a) have a single solution (b) will have no solutions.