Get math assignment help instantly

To get math assignment help instantly is now easy with online tutoring services on web; any topic related to math can be discussed with the tutors so it is very useful for students to solve their problems in seconds by assignment help from ExpertsMind.

Let x = [a_ij], I = 1, 2, …, r; j = 1, 2, ….s,

and, y = [b_jk], j = 1, 2, …., p; k = 1, 2, ….,q

be two r × s and p × q matrices in that order such that the number of rows of B is the similar as the number of columns of A.

After that the product of these two matrices is classified as an r × q matrix C = AB = [c_ik], I = 1, …., r; k = 1, …,qp

here c_ik = a_i1 b_1k + a_i2 b_2k + ….. + a_in b_nk = b_ik

= Sum of the products of the factors of i^th row and j^th columns of A with the equivalent elements of j^th row and k^th columns of B.

Reminder: c_ik is found by multiplying the elements in the i^th row of A with the equivalent elements in the k^th column of B and then adding them.

The product matrix AB will contain r rows and q columns, i.e. if A is an r × q matrix and B is s × q matrix, after that AB is an r × q matrix.

In the product AB, A is well-known pre-factor and B as post-factor.

Therefore we notice that the product AB is defined if and only if numerous columns of the pre-factor is equal to the number of rows of the post-factor.

Two matrices A and B are said to be contented for multiplication if the number of columns of A is equal to the number of rows of B.

Reminder: It is significant to note that there can be matrices which are not contented for multiplication and in that case we state that the multiplication of the matrices is not distinct. We consider a few instances to illustrate the above data.

Matrix Scalar Multiplication

The scalar multiple kA of a matrix A (square or rectangular) through a scalar k is a matrix obtained by multiplying each element of A by the scalar k.

For instance: the scalar multiple of the matrix A by k.

Negative of a matrix: The negative of a matrix A is – A.

We portray – A = (–1) A

Comments

Earning And Investment Decisions By Financial Manager

The tasks of Financial Manager can usually be categorized into two: Managerial Finance Functions: Require skilful planning, control and execution of the financial behavior. It consists of noteworthy managerial finance tasks. These are as: (a) Investment of Long-term asset-mix options: Such decisions (also referred to as capital budgeting judgment) relates to the allotment of funds along with investment projects. They refer to the firm's option to commit current finances to the purchase of permanent assets in hope of future cash inflows from these projects. The investment applications are evaluated in terms of both risk and predictable arrival. (b) Financing decisions: Financing decision means the decision on the sources of finances to invest on finance projects. The finance manager ought to decide the proportion of justice and debt. The mix of debt & equity affect the firm's price of financing as well the financial risk....

Reactions Accompanied by Thermodynamic Processes

A thermodynamic property elucidates considerable characteristics of a substance. The knowledge of these properties is necessary to the understanding of the thermodynamics. The quantity which is either a feature of a whole system or is a function of place that is constant and does not differ rapidly over microscopic distances, apart from possibly for unexpected changes at boundaries among phases of the system; illustrations are pressure, temperature, volume, surface tension, concentration, and viscosity. This is also termed as macroscopic property. In order to bring through a program of finding the modifications in the different thermodynamic functions which accompany reactions—like enthalpy, entropy, and free energy—it is frequently helpful to know such quantities separately for each of the materials entering into the reaction. For illustration, when the entropies are known independently for the reactants and products, then the entropy alter for the reaction is merely the d...

Antibiotics: Hindering the augmentation of Micro-organisms

The search for antibiotics begin in late 1880’s, with the acceptance of the germ hypothesis of diseases. In the mid of 1800 the Hungarian physician Ignatz Semmelweis and the English physician Joseph Lister generated some of the primary microbial control practices. Whenever the body’s normal defenses can’t prevent or overcome a disease, it is frequently treated with chemotherapy. Antimicrobial drugs act by hindering with the augmentation of microorganisms. Furthermore, it has to act in the host. Hence, their effects on the cells and tissues of the host are significant. The ideal antimicrobial drugs kill the injurious microorganisms without harming the host. The mechanism of inhibition is termed as antibiosis and from this term comes the word Antibiotic, a substance generated by certain microorganisms. Certain drugs have a narrow spectrum of microbial activity and certain affect a wide range of gram positive and gram negative bacteria and are termed as broad spectrum a...

ask an Expert 24/7

Search This Blog