As you have not mentioned that where to find solution I have assumed the solution space to be Z, the set of integers. However similarly you can show this for N, the set of natural numbers.
1. Find all solutions to the system x1 + 2x2 + 3x3 = 8 1 x1 - x2 + 3x3 = 5 =>{801_ ) but ke 2. Is a basis for R3? 13 12
Find the number of solutions to x1 + x2 + x3 + x4 = 200 subject to xi E 220 (1 < i < 4) and x3, x4 < 50 in two ways: (i) by using the inclusion-exclusion principle, and (ii) using generating functions.
3. Two solutions of the following linear equation system are x1, X2, where Xi = (1,1,-3,1), x2-x1 + xd xd that makes cTx2 - cTx1 - 1, where c [1 1 2 1] Find every Ax=11 2 2 3 |x=b 3. Two solutions of the following linear equation system are x1, X2, where Xi = (1,1,-3,1), x2-x1 + xd xd that makes cTx2 - cTx1 - 1, where c [1 1 2 1] Find every Ax=11 2 2 3 |x=b
Find all solutions to the system using the Gauss-Jordan elimination algorithm. X1 + 2x2 + 2x3 = 12 4x3 24 442 + 12x3 = 24 + 4x2 + 8x1 4x1 + Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The system has a unique solution. The solution is x1 = X2 = X3 = X2 = X3 = S. - <s<00. OB. The system has an infinite number of...
Min 2x1 + x2 s.t. x1 + x2 ≥ 4 x1 – x2 ≥ 2 x1 – 2x2 ≥ –1 x1 ≥ 0, x2 ≥ 0 Please solve the linear program graphically, showing the objective function, all constraints, the feasible region and marking all basic solutions (distinguishing the ones that are feasible).
Use the simplex algorithm to find all optimal solutions to the following LP. max z=2x1+x2 s.t. 4x1 + 2x2 ≤ 4 −2x1 + x2 ≤ 2 x1 ≥1 x1,x2 ≥0
Find a basis for the subspace of R3R3 consisting of all vectors [x1 x2 x3] such that 8x1+5x2−2x3=08x1+5x2−2x3=0. Hint: Notice that this single equation counts as a system of linear equations; find and describe the solutions.
Determine all the integer solutions to the equation X1 + X2 + X3 + X4-7 where xj 2 0 for all i - 1,2,3,4
Let X1 and X2 have joint PDF f(x1,x2)=x1+x2 for 0 <x1 <1 and 0<x2 <1.(a) Find the covariance and correlation of X1 and X2. (b) Find the conditional mean and conditional variance of X1 given X2 = x2.
f(x1, x2) = -2(x1)(x2)+ (x1)^3 + (x2)^3 a) Find a maximum in the region where x1 ≤ 1 and x2 ≤ 1 (Hint: remember to check what happens when x1 = 1 and x2 = 1) b) Now consider (x1, x2) ∈ R 2 , that is, the entire two-dimensional space where x1 and x2 are in[−∞,+∞]. Is there a maximum?