# a 2 pts Verify through computation that if A = 3 0 2 - 1 ,...

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Math for Econ II, Written Assignment 5 (28 points) Due Friday, March 14th New York University Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will not be given any credit. Write your name and recitation section number. Staple your homework if you have multiple pages! 1. (a) (2 pts) Verify through computation that if A = 3 0 2 - 1 , then A - 1 = 1 / 3 0 2 / 3 - 1 (b) (2 pts) Verify through computation that if A = 1 1 - 3 2 1 - 3 2 2 1 , then A - 1 = - 1 1 0 8 / 7 - 1 3 / 7 - 2 / 7 0 1 / 7 (c) (2 pts) Use the inverse from (b) to solve the system x + y - 3 z = 10 2 x + y - 3 z = 14 2 x + 2 y + z = 7 . 2. (a) (2 pts) Find the inverse of - 3 5 4 - 7 . (b) (4 pts) Find all values of x for which the following matrix is invertible: x 2 3 x - 1 . 3. Data interpolation has many applications. In this problem, we will find the third degree polynomial P ( x ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 which passes through the points ( - 2 , 6), ( - 1 , 4), (1 , 6), and (2 , 22). (a) (3 pts) Show that since P ( - 2) = 6,