Thursday, April 24, 2014

The Matrix… Symbolab Version

Matrix, the one with numbers, arranged with rows and columns, is extremely useful in most scientific fields.   There are a number of basic operations that can be applied to modify matrices such as matrix addition, scalar multiplication, matrix multiplication and transposition.  Solving matrices is not that bad once you get the hang of it, but, the larger the matrix the more tedious the calculation becomes.

Tedious?  not quite, let’s jump in and see how Symbolab can help you solve matrices.
To start with we’ve added easy to use buttons to type in matrices; this is how it looks like:

Matrices of the same size can be added or subtracted element by element.
Here’s an example (click here):

Not too complicated, just takes a lot of work

Two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second.  If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B.

To make this simple, let’s take a look at an example (click here):

Multiplying matrices is no fun…

To transpose a matrix simply swap the rows and columns
Here’s an example (click here):

The trace of an n-by-n square matrix is defined to be the sum of the elements on the main diagonal
Here’s an example (click here):

Matrix takes practice, click here to start.