## Posts Tagged ‘Product’

## Product of Two Matrices

**Product of Two Matrices**

Let *A *be an m n matrix and let *B *be an n k matrix. To find the element in

the *i*th row and *j*th column of the **product matrix ***AB*, multiply each element in

the *i*th row of *A *by the corresponding element in the *j*th column of *B*, and then

add these products. The product matrix *AB *is an m k matrix.

Example:-

A = and B

Then AB =

## Product of a Matrix and a Scalar

**Product of a Matrix and a Scalar**

The product of a scalar *k *and a matrix *X *is the matrix *kX*, each of whose elements

is *k *times the corresponding element of *X*.

For examples,

## Product Rule for Exponents

**Product Rule for Exponents**

** **

If *m *and *n *are natural numbers and *a *is any real number, then

* a ^{m}. a^{n} = a^{m+n}.*

** **

In words, when multiplying powers of like bases, keep the same base

and add the exponents.