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1. Determine if the following two-, three-, and four- dimensional sets for given pariables xy, xz,...
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether...
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether they form a basis of the vector space to which they belong. s 10110 -1 ) / -1 2) / 2 1 17 ) } in M2x2(R). "11-21 )'(1 1)'( 10 )'(2 –2 )S (b) {23 – X, 2x2 +4, -2x3 + 3x2 + 2x +6} in P3(R) (the set of polynomials of degree less than 3. (c) {æ4—23+5x2–8x+6, – x4+x2–5x2 +5x-3, x4+3x2 –...
Please answer using MATHLAB. I need the code and the answer. Thanks, Use MATLAB or Scilab...
Please answer using MATHLAB. I need the code and the answer.
Thanks,
Use MATLAB or Scilab to perform the following matrix operations 1) Find the determinant of ſi 7 -2 31 5 -1 9 13 2 51 31 4 6 18 -4 21 2) Find the inverse (A-2) of ſi 7 -2 3] 5 -1 9 13 2 51 314 6 18 -4 2' 3) Given the following set of linear equations X, + 2 x, – x3 + xy...
d) x(t/2) 3) Given x (t) = cost, x2(t) = sin it, and xz(t) = xy(t)...
d) x(t/2) 3) Given x (t) = cost, x2(t) = sin it, and xz(t) = xy(t) + x2(t). a) Determine the fundamental periods T and T, of signals x (t) and x2(t). b) Is xz(t) periodic, which if periodic requires Tz = nt = mT2, for some integers n and m. c) Determine the powers of Px,, Pxz, and Pxof signals x (t),xz(t) and xz(t). Answer: a T. 2 2 h not neriodic is not rational P = P =...
1. (20 pts.) Consider the following linear program: max 4x4 +xz+5x3 +3x4 s.t. *1 -X2 -X3...
1. (20 pts.) Consider the following linear program: max 4x4 +xz+5x3 +3x4 s.t. *1 -X2 -X3 +3X, 51 5x +xz+3X3 +8X555 -X2 +2x2+3x3 -5x53 It is claimed that the solution x* = (0,14,0,5) is an optimal solution to the problem. Give a proof of the claim. Do not use the simplex method to solve this problem.
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>....
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
Solve the following linear programming problem using Two Phase method [12M] Maximize z = 3X1 -...
Solve the following linear programming problem using Two Phase method [12M] Maximize z = 3X1 - 3X2 + X3 Subject to X; + 2x, - xz 25 - 3x; – x2 + x3 54 47, X2, X3 20.
Question 2. 20 marks Determine whether the following sets form subspaces of the standard 2-dimensional Euclidean...
Question 2. 20 marks Determine whether the following sets form subspaces of the standard 2-dimensional Euclidean space (R%. +. :): (a) A = {(11.12)|*1 = -2). (b) B = {(21,12) 2119 = 0). (e) C = {(1, 12) 12 = 2x;}. (d) D = {(2,12) ||*|-|-2), where x. denotes the absolute value of x, for i=1,2. (e) E = {(*1,22) | } = =3)
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...
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...
Determine whether or not the field F (x,y,z) = (y4_47, 4x4°+62" - XZ, 12yz +10-xy) is...
Determine whether or not the field F (x,y,z) = (y4_47, 4x4°+62" - XZ, 12yz +10-xy) is conservative. If so, find (x, y, z), a Potential function for Be sure to check your answer! out Form om POP y-plane 20.) for both parts of this problem, the vector field is: < 2x + y, x-2y) & the corve is x=y² from er in din F(x,y) ..3 Do ad on A.) Compute F.Tds - Di de one of the following ways: See...
1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets...
1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets of numbers. Consider the problem of finding their intersection, i.e., the set C of all the numbers that are in both A and B. a. Design a presorting based algorithm for solving this problem and determine its efficiency class. 2. Estimate how many searches will be needed to justify time spent on presorting an array of 103 elements if sorting is done by mergesort...
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether they form a basis of the vector space to which they belong. s 10110 -1 ) / -1 2) / 2 1 17 ) } in M2x2(R). "11-21 )'(1 1)'( 10 )'(2 –2 )S (b) {23 – X, 2x2 +4, -2x3 + 3x2 + 2x +6} in P3(R) (the set of polynomials of degree less than 3. (c) {æ4—23+5x2–8x+6, – x4+x2–5x2 +5x-3, x4+3x2 –...
Please answer using MATHLAB. I need the code and the answer.
Thanks,
Use MATLAB or Scilab to perform the following matrix operations 1) Find the determinant of ſi 7 -2 31 5 -1 9 13 2 51 31 4 6 18 -4 21 2) Find the inverse (A-2) of ſi 7 -2 3] 5 -1 9 13 2 51 314 6 18 -4 2' 3) Given the following set of linear equations X, + 2 x, – x3 + xy...
d) x(t/2) 3) Given x (t) = cost, x2(t) = sin it, and xz(t) = xy(t) + x2(t). a) Determine the fundamental periods T and T, of signals x (t) and x2(t). b) Is xz(t) periodic, which if periodic requires Tz = nt = mT2, for some integers n and m. c) Determine the powers of Px,, Pxz, and Pxof signals x (t),xz(t) and xz(t). Answer: a T. 2 2 h not neriodic is not rational P = P =...
1. (20 pts.) Consider the following linear program: max 4x4 +xz+5x3 +3x4 s.t. *1 -X2 -X3 +3X, 51 5x +xz+3X3 +8X555 -X2 +2x2+3x3 -5x53 It is claimed that the solution x* = (0,14,0,5) is an optimal solution to the problem. Give a proof of the claim. Do not use the simplex method to solve this problem.
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
Solve the following linear programming problem using Two Phase method [12M] Maximize z = 3X1 - 3X2 + X3 Subject to X; + 2x, - xz 25 - 3x; – x2 + x3 54 47, X2, X3 20.
Question 2. 20 marks Determine whether the following sets form subspaces of the standard 2-dimensional Euclidean space (R%. +. :): (a) A = {(11.12)|*1 = -2). (b) B = {(21,12) 2119 = 0). (e) C = {(1, 12) 12 = 2x;}. (d) D = {(2,12) ||*|-|-2), where x. denotes the absolute value of x, for i=1,2. (e) E = {(*1,22) | } = =3)
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...
Determine whether or not the field F (x,y,z) = (y4_47, 4x4°+62" - XZ, 12yz +10-xy) is conservative. If so, find (x, y, z), a Potential function for Be sure to check your answer! out Form om POP y-plane 20.) for both parts of this problem, the vector field is: < 2x + y, x-2y) & the corve is x=y² from er in din F(x,y) ..3 Do ad on A.) Compute F.Tds - Di de one of the following ways: See...
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