a) (2 pts) Write down the linear system of equations for the coefficients of a degree...

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a) (2 pts) Write down the linear system of equations for the coefficients of a degree 2 polynomial f(x) = ax+bx+c, that would interpolate the points (-2, -1), (-1, -4), (1, -2) and (3, 1). b) (2 pts) Explain why the system you found in a) is inconsistent and and as a result does not have a polynomial of degree 2 that passes through all the points. c) (2 pts) Find and write down the normal equation for the system you found in a). (d) (2 pts) Find the polynomial of degree 2 that best fits the points in a). For full credit, show the main steps of your work and your reasoning. You may use Matlab for parts c) and d). If you do so, you need to include screenshots of the commands you use, and the results of these commands. For part c) you need to write out the normal equation by hand, even though you may use Matlab to do the math computations. For part d) you need to write out the polynomial by hand, even though you a) (2 pts) Write down the linear system of equations for the coefficients of a degree 2 polynomial f(x) = ax+bx+c, that would interpolate the points (-2, -1), (-1, -4), (1, -2) and (3, 1). b) (2 pts) Explain why the system you found in a) is inconsistent and and as a result does not have a polynomial of degree 2 that passes through all the points. c) (2 pts) Find and write down the normal equation for the system you found in a). (d) (2 pts) Find the polynomial of degree 2 that best fits the points in a). For full credit, show the main steps of your work and your reasoning. You may use Matlab for parts c) and d). If you do so, you need to include screenshots of the commands you use, and the results of these commands. For part c) you need to write out the normal equation by hand, even though you may use Matlab to do the math computations. For part d) you need to write out the polynomial by hand, even though you