Under what circumstances would the matrix arising in, Computer Engineering

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Under what circumstances would the matrix arising in

Problem

1. What values of a, b, c minimize the least-squares error in using the function f(x) = ax logx +bx + c approximate the observations f(1) = 0, f(4) = 13, f(8) = 41?

2. Excluding the Gaussian elimination phase, how many multiplications are involved in using the method of least squares to find M coefficients based on N observations?

3. Under what circumstances would the matrix arising in least-squares curve fitting be singular?

4. Does the least-squares method work if two different observations are included for the same point?

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