Express the following in the SIGMA notation:
a. x1 +x2 +x3 +x4 +x5
b.x1 +2x2 +3x3 +4x4 +5x5
Express the following in the SIGMA notation: a. x1 +x2 +x3 +x4 +x5 b.x1 +2x2 +3x3...
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the standard matrix representation A of T b.) find the basis of Col(A) c.) find a basis of Null(A) d.) is T 1-1? Is T onto?
Consider the following linear transformation T: RS → R3 where T(X1, X2, X3, X4, X5) = (x1-X3+X4, 2X1+X2-X3+2x4, -2X1+3x3-3x4+x5) (a) Determine the standard matrix representation A of T(x).
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25 Problem 1 (20 pts) Consider...
Consider the following linear transformation T: R5 → R3 where T(X1, X2, X3, X4, X5) = (*1-X3+X4, 2X1+X2-X3+2x4, -2X1+3X3-3x4+x5) (a) Determine the standard matrix representation A of T(x). (b) Find a basis for the kernel of T(x). (c) Find a basis for the range of T(x). (d) Is T(x) one-to-one? Is T(x) onto? Explain. (e) Is T(x) invertible? Explain
Consider the mathematical program max 3x1 x2 +3x3 s.t. 2X1 + X2 + X3 +X4-2 x1 + 2x2 + 3x3 + 2xs 5 2x1 + 2x2 + x3 + 3x6 = 6 Three feasible solutions ((a) through (c)) are listed below. (b) xo) (0.9, 0, 0, 0.2,2.05, 1.4) (c) xo) (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution.
Consider the following LP problem max z = x1 +2x2 + x3 + x4 s.t. x1 + 2x2 + x3 く2 +2x3 く! X1, x2, x3, x4 20 a) Obtain the dual formulation of the LP.
Solve using Gauss Jordan 3) Given the following set of linear equations x, +2x2-x3 +x4=5 -xi-2x2-3x3 + 2x4 = 7 x, +x2 + x3+x4=10
For the data x1 = -1, x2 = -3, x3 = -2, x4 = 1, x5 = 0, find ∑ (xi2).
)Consider the non-negative integer solutions to x1 + x2+ x3 + x4 + x5 = 2020. (A) How many solutions does Equation (1) have satisfying 0 ≤ x1 ≤ 100? Explain. (B) Remember to explain your work. How many solutions does Equation (1) have satisfying 0 ≤x1 ≤ 100, 1 ≤x2 ≤ 150, 10 ≤x3 ≤ 220?
Write a latex solution for #2 please. 1. Use back substitution to solve each of the following systems of equations: (a) -3X2 = 2 2x2 = 6 (b) x1 +x2 +x3 = 8 2x2 + x3 = 5 3x3 = 9 (c) x1 + 2x2 + 2x3 + X4 = 3x23 2x41 4X4 = (d) X1 + X2+ X3+ X4+ X5 = 5 2x2 + X3-2x4 + X5=1 4x3 + x4-2x5 = 1 2. Write out the coefficient matrix for...