You are required to find the unique polynomial, y = f(x), of degree 6 that interpolates...

 

 

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You are required to find the unique polynomial, y = f(x), of degree 6 that interpolates the following 7 points (-3, -262), (-2, 3), (-1, 3), (0, -1), (1, 0), (2, 3), (3, -127). (a) (3 pts) Write down the linear system that you need to solve to find the coefficients of this polynomial. Also write down the augmented matrix of this system. (b) (4 pts) Solve the system from part (a) to find the coefficients of the polynomial and write down the polynomial. (Write your answer to 3 decimal places if necessary.) You can use ONE of the two methods below: (i) You can solve the system "by hand", in which case you will need to show at least 5 of the intermediate reduction steps, and include the row operations that were used. (ii) You can use Matlab to do the work. For credit using this approach, you must take screenshots of the Matlab commands you used and screenshots of the corresponding Matlab output. For each command, add a brief comment explaining what was done. Take one screenshot for each Matlab command/Matlab output pair. Take the screenshots of the Matlab command/Matlab output pairs and not the entire screen. You need to follow these instructions for full credit. You are required to find the unique polynomial, y = f(x), of degree 6 that interpolates the following 7 points (-3, -262), (-2, 3), (-1, 3), (0, -1), (1, 0), (2, 3), (3, -127). (a) (3 pts) Write down the linear system that you need to solve to find the coefficients of this polynomial. Also write down the augmented matrix of this system. (b) (4 pts) Solve the system from part (a) to find the coefficients of the polynomial and write down the polynomial. (Write your answer to 3 decimal places if necessary.) You can use ONE of the two methods below: (i) You can solve the system "by hand", in which case you will need to show at least 5 of the intermediate reduction steps, and include the row operations that were used. (ii) You can use Matlab to do the work. For credit using this approach, you must take screenshots of the Matlab commands you used and screenshots of the corresponding Matlab output. For each command, add a brief comment explaining what was done. Take one screenshot for each Matlab command/Matlab output pair. Take the screenshots of the Matlab command/Matlab output pairs and not the entire screen. You need to follow these instructions for full credit.