Please solve all systems of equations using the method that involves finding the inverse of a...

 

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Please solve all systems of equations using the method that involves finding the inverse of a square matrix. Use MATLAB to find the inverses. You don't have to show your MATLAB work, but do write down the matrices that you use and the corresponding inverses. 1. Find the equation of a parabola that passes through the points (0,2), (2,5), and (10, -12). 2. Find a polynomial of smallest degree that passes through the points (2, 4), (4, 1), (0, 10), (5,2), (-1,20). 3. Find a polynomial of smallest degree that passes through the points (2002, 20), (2004, 5), (2000, 4), (2005, 12). (Hint: to avoid taking powers of large numbers, shift all these points to the left so the x-coordinates are not so big. Then when you find your answer, shift the polynomial back to the right so it contains the given points.) 4. OPTIONAL BONUS PROBLEM. Let (x, y), (x2, Y2), (x3, Y3) be any three points with 3. Write down the 3 3 matrix A that you obtain using the Prove that det A = 0. X1 X2, X1 x3, x2 method of #1 above. Please solve all systems of equations using the method that involves finding the inverse of a square matrix. Use MATLAB to find the inverses. You don't have to show your MATLAB work, but do write down the matrices that you use and the corresponding inverses. 1. Find the equation of a parabola that passes through the points (0,2), (2,5), and (10, -12). 2. Find a polynomial of smallest degree that passes through the points (2, 4), (4, 1), (0, 10), (5,2), (-1,20). 3. Find a polynomial of smallest degree that passes through the points (2002, 20), (2004, 5), (2000, 4), (2005, 12). (Hint: to avoid taking powers of large numbers, shift all these points to the left so the x-coordinates are not so big. Then when you find your answer, shift the polynomial back to the right so it contains the given points.) 4. OPTIONAL BONUS PROBLEM. Let (x, y), (x2, Y2), (x3, Y3) be any three points with 3. Write down the 3 3 matrix A that you obtain using the Prove that det A = 0. X1 X2, X1 x3, x2 method of #1 above.