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What is matrix form of the system of linear equation?
Ax=b is A is [mxn] matrix; x column vector with n entries; b column vector with m entries Apply the Frobenius theorem in the solution of the system of linear equation? -System of linear equations has at least one solution if only if the rank of matrix of system is equal to the rank of augmented matrix of system. -The rank of matrix is number of linear independent rows(columns) in matrix -The rank of matrix can be set as number of nonzero rows(columns) in row echelon form of matrix 4. Describe the Gauss-Jordan total elimination is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix. System of linear equations: Bx=Iy=y If B has an inverse, then multiplying on the left bvy B-1 yields. Goal of the elimination one variable is isolated in each row. Describe the algorithm of finding the inverse matrix? -Form an augmented nx2n matrix by writing the [nxn] identity matrix right of A’’ -Performing row operations on the augmented matrix transform A to the identity matrix I. -The matrix I that we added will be automatically transformed to A-I. If it is impossible to transform A into identity, A is not invertible. Which are the phrase of the decision making process? -Intelligence, design, choice, implement Describe the Anthony’s classification of the decision making. Draw the Anthony’s pyramid? -Strategic Planning -Tactical Planning -Operations Control. Which are typical features of the strategic tactic and operational control. Which are the typically decision in those group? *. Strategic Planning: - Is concerned mainly with establishing managerial policies. -Major capital investments. -These strategic decisions have long-lasting effect sand requires the consideration of uncertainties and risk attitudes. -Are resolved at fairy high managerial levels *. Tactical Planning: - Effective allocation of resources (production m storage) to satisfy demand and technological requirements, taking into account the costs and revenues associated with operation of the resources available to the firm. -Medium range time horizon - Require significant aggregation *. Operations Control: -Deal with the day-to-day operational and scheduling decisions -Typical decisions: The assignment of customer orders in the work shop, inventory accounting and inventory controls activities. Compare programmed and non programmed decisions? -Programmed: Are those that occur routinely and repetitively -Non programmed: Are complex, unique and unstructured Compare the main kinds of the mathematical models(operational exercise, gaming, simulation, analytical) a. Operational exercise: Is an inductive learning process, characteristic of empirical research in the nature sciences, in which generalizations are drawn from particular observations of a given phenomenon. b. Gaming: Provides the responsive mechanism to evaluate the effectiveness of proposed alternatives c. Simulation: Are similar to gaming models except that all human decision-maker are removed from the modeling process. d. Analytical: Represented completely in mathematical term, normally by meant of a criterion or objective which we seek to Maximize or Minimize
Which are the mian types of variablesin the mathematical model -Decision variables -Parameters -Exogenous variables -Polocies and Constrains -Performance Measures - Intermediate Variables |
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