Explain the terms: Unique matrix, reduced echelon form, coefficient matrix, right hand side vector (RHS), augmented matrix ?

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Explain the terms: Unique matrix, reduced echelon form, coefficient matrix, right hand side vector (RHS), augmented matrix?

Unique matrix = identity matrix: The identity matrix of order m, written Im is a square (m-by-m) matrix with ones along the diagonal and zeros elsewhere.

Reduced echelon form: -The coefficient matrix is square(mxn)

All its entries on the main diagonal to 1(pivot) and all the entries below the main diagonal zero

Row reduction-substeps

-Find the left most non zero column of the matrix

-Make sure, by applying row operations, if necessary, that the first(upper) entry of this column is equal to 1.This entry will be called pivot

-Kill(make them 0) all non zero entries below the pivot by adding an approximate multiple of the first row from the rows number 2, 3

Coefficient matrix: The matrix formed by the coefficients in a linear system of equations(m-by-n matrix)

Augmented matrix: The matrix forms of linear system equations obtained from the coefficient matrix. It is created by adding an additional column for the constants on the right of the equal signs. The new column is set apart by a vertical line

RHS: Is a column vector with m entries called constants vector.

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.