Posts Tagged ‘Product’

Product of Two Matrices

Product of Two Matrices

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

the ith row and jth column of the product matrix AB, multiply each element in

the ith row of A by the corresponding element in the jth column of B, and then

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


A = \begin{bmatrix}  2 & 3 &-1 \\  4 & 2 & 2  \end{bmatrix} and B\begin{bmatrix}  1\\  8\\  6  \end{bmatrix}.

Then AB = \begin{bmatrix}  2 & 2 & -1\\  4 & 2 & 2  \end{bmatrix}\begin{bmatrix}  1\\  8\\  6  \end{bmatrix} = \begin{bmatrix}  20\\  32  \end{bmatrix}

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,

(-3)\begin{bmatrix}  2 & -5\\  1& 7  \end{bmatrix}=\begin{bmatrix}  -6 & 15\\  -3& -21  \end{bmatrix}.


Product Rule for Exponents

Product Rule for Exponents


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


   am. an = am+n.


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

and add the exponents.