1. Problem 1. Compute the exact numerical value of the scalar quantity defined as, 35 The...
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
Problem #1 Write a user-defined function called mysecant. (Not an an please!) The purpose of the function is: Given two points, compute the line between them and so where the corresponding y3-0. If there is no solution, Hint: The governing equations are: (y3-y1)-(y2-y1) / (x2-x1) * (x3-x1) if y3-0, then solve for x3, and so, x3-x1-y1 * (x2-x1) / (y2-y Inputs: x1, y1, x2, y2 Output: x3
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
35 Given a boundary-value problem defined by =i+1, 0<r <1 subject to (0)= 0 and 0(1)= 1, use the finite difference method to find (0.5). You may take A = 0.25 and perform 5 iterations. Compare your result with the exact solution.
Question 1: Given the initial-value problem 12-21 0 <1 <1, y(0) = 1, 12+10 with exact solution v(t) = 2t +1 t2 + 1 a. Use Euler's method with h = 0.1 to approximate the solution of y b. Calculate the error bound and compare the actual error at each step to the error bound. c. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual value...