Consider the following nonhomogeneous system. (Enter any column vector as a row vector.) 3 x' = x + -4t2 t + 3, Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = 4,-2 You got it! Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue. If there is only one repeated eigenvalue, enter the eigenvector in each answer blank.) Κι = (-1,1) K₂ (1,1) That's right! You're right! Find the general solution of the given system. x(t)=C₁-1,1)e 2¸ 4t - C₂(1,1)e¹² +
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- For the next 6 numbers: Refer to the Management Scientist output of a maximization LP problem. The constraints are defined as follows: Constraint 1: advertising budget ( ) Constraint 2: sales force availability ( ) Constraint 3: production level (=) Constraint 4: retail stores requirement ( ) Optimal Solution Objective Function Value - Variable. Constraint X1 X2 X1 X2 X3 X4 X3 X4 1 2 Variable 1 2 3 3 4 OBJECTIVE COEFFICIENT RANGES 4 Constraint RIGHT HAND SIDE RANGES Value Slack/Surplus Lover Limit 25.000 425.000 150.000 0.000 84.000 50.000 No Lover Linit No Lover Linit Lover Limit 48450.000 0.000 25.000 0.000 0.000 4950.000 1775.000 515.000 0.000 Reduced Costs Dual Prices Current Value 90.000 84.000 70.000 60.000 Current Value 0.000 0.000 0.000 45.000 5000.000 1800.000 600.000 150.000 3.000 0.000 60.000 -17.000 Upper Limit No Upper Linit 90.000 87.000 105.000 Upper Linit 5850.000 No Upper Limit 603.571 200.000typing clearly urjentBad simulations Explain why each of the followingsimulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to representthe number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a ran-dom digit, using an odd digit to represent a good shot and an even digit to represent a miss.c) Use random numbers from 1 through 13 to represent thedenominations of the cards in a five-card poker hand.
- Maximize z=4x+5y Subject to: x+y<or=4 x-y>or=-2 x<or=3 x>or=0, y>or=0Show that Jσ_(ij)D_(ij)=T_(iL)F_(iL˙)=S(AB)E_(AB˙) [Hints: (a) to prove the first equation, use the relationship between F_(iL)˙ and L_(ij), and expand L_(ij) into symmetric and antisymmetric parts. Note the symmetry of σ_(ij). (b) To prove the second equation, first express E_(AB)˙ using F_(iL), then take the time derivative. Substitute into the definition of S_(AB )in index form and simplify.]Find the Inverse Laplace Transform of Y(s) = 12 (s+5)*
- 416 A=[-4 0-7]. 00-3 Determine the multiplicity of each eigenvalur and a basis for each eigenspace of the given matrix a. Hence determine the dinension of each eigenspace and state whether the matrix is defective or nondefectiveplease note needed to calculate inverse of f prime at x = 1/2.Below shown is a logical representation of an index table built on columnA SearchKey Record Location G005234 1 G098967 G099537 3 9 G136790 13 Based on the provided information, which one of the following statements is correct? O a. Without seeing the actual table, based on index alone it is not possible to determine whether or not table is sorted by columnA O b. The table containing ColumnA is physically sorted by ColumnA O c. Insufficient information to determine whether or not the table is sorted by ColumnA O d. The table containing ColumnA is not physically sorted by ColumnA
- Solve (xex + y) dx − x dy = 0Select the appropriate description of the distribution 10 | 0, 0, 2, 2, 3, 3, 4, 5, 5, 6, 8 12 | 0, 3, 4, 5, 8 13 | 0, 4, 6 14 | 1, 3 Legend 11 | 0 represents 100 Uniforms Bell shaped Skewed right Skewed leftUsing back-substitution, show that an ARMA(1, 1) model may be written as eitheran AR or an MA model.