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Home Question Bank Other Archive 2024 December 23

Other Questions from Dec 23,2024

Browse the Other Q&A Archive for Dec 23,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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1. Find eigenvalues and eigenvectors of the following matrices: \[ A=\left(\begin{array}{rr}-1 & 0 \\ 1 & -1\end{array}\right), \quad E=\left(\begin{array}{lll}2 & 0 & 1 \\ 0 & 3 & 4 \\ 0 & 0 & 1\end{array}\right) \] an you tell whether the matrix \( \quad A=\left[\begin{array}{lr}9 & -15 \\ -15 & 25\end{array}\right] \quad \) is positive definite? Exorcise 3.11 . Let \( \mathrm{A}=\left(\begin{array}{ccc}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 6 & -5\end{array}\right) \). Find the matrix obtained from \( A \) by applying the following elementary row operation. \( \begin{array}{lll}\text { a. } R_{1} \leftrightarrow R_{3} & \text { b. } R_{2} \rightarrow R_{2}-4 R_{1} & \text { c. } R_{3} \rightarrow \frac{1}{3} R_{3}\end{array} \) Which of the following is not correct? (a) Duality does not play any role in the post - opti mal analysis of on LPP. (b) The optimum simplex table provides informa tion about the status and worth of the resources in addition to the optimum values of the decision variables. (c) In the optimum solution of a profit maximization LPp, the total (optimum) profit must be equal to the total wortiof the resources. (d) To write the dual problem, it is necessary that its primal LPP must have all its variables as greater than or equal to zero. (xii) Costs in objective function in phase 2 of two phase method are (a) Actual coefficients (b) Zero (c) -1 (d) None of these (xiii) The right hand side constant of a constreintin a primal problem appears in the corresponding dual as : (a) A coefficient in the objective function (b) A right-hand side constant of a constraint in a (c) An input-output coefficient (d) None of these Describe classification of models by function.
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