please do 17-18

> 13. The data (1, -3), (2,1) and (3,2) is gathered as part of an experiment. Find the line of best least squares fit for this data, and then use this line to approximate the value of y associated with x = 5/2. 14. Give an interpolating polynomial of degree 2 for the data given in problem 13. 15. Use elementary row operations to find the inverse of the matrix 2 1 0 0 16. Let V = span (" ). (3 ) .(3 a. Find all vectors v E V with length 1. b. Use the Gram-Schmidt process to find an orthogonal basis for V. 17. The data (-1,4), (0,2), (2, -3), (4, -3) and (7,4) was gathered as part of an experiment. a. Plot this data. b. Set up a system of equations that can be solved to find the values a, b and c so that y = a + bx + cx2 is the best least squares fit for this data. Do not solve the system. 18. Define the function T : P2 - P2 via T(g(x)) = (2x2-1)g'(x) + g(x). a. Give T(x2 - 3x + 2). b. Find (if possible) all functions f (x) E P2 for which T(f (x) ) = -2x2 - x - 1. 19. Find the eigenvalues and eigenspaces associated with the matrix (2 72). 20. A is a real 2 X 2 matrix and 1 - i is an eigenvalue of A. Suppose ( ) is an eigenvector associated with the eigenvalue 1 - i. Give the matrix A. Type here to search 64F Sunny ~ 9 6 ( ) 2:05 PM 11/29/2021 E