What is a Matrix

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Hey welcome to the first lecture on linear algebra our linear algebra journey starts with matrices.

Do you know what’s a matrix.

A matrix is a collection of numbers ordered in rows and columns like this one for example.

This matrix contains the numbers 5 12 6 minus 3 0 and 14.

Each of these values is an element of the matrix.

So our matrix has a total of six elements.

To make it clear we are dealing with a matrix.

We put all the elements in brackets we would normally denote a matrix with a capital letter for instance

a our matrix A has two rows and three columns in linear algebra rows and columns are the two dimensions

of the matrix A has two rows and three columns.

So we say its dimensions are two and three or better.

A is a two by three Matrix Normally we would take note on that and put it below the letter A OK.

Major CS may seem like tables and spreadsheets at first.

However the purpose of matrices is not simply to store values but to be main characters in mathematical

operations.

Two major cities can be summed subtracted multiplied and divided.

So linear algebra is similar to algebra and the types of operations there are but differs in how and

when these operations are implemented and if they are permitted at all we will discuss all of that at

length in this section.

OK a matrix can only contain numbers symbols or expressions with the idea that the latter two are nothing

more than a generalized representation of numbers.

For instance the collection of these six symbols A B C D E F.

Show a different two by three Matrix.

Say B.

Here’s another one.

C C has 4 elements and is a two by two Matrix.

It’s incumbent however are not values but expressions great what about the size of a matrix.

Major CS can be of any size in the general case we are talking about an Mbai and matrix.

If a is an Mbai and matrix then this means that as m rows and columns sometimes we need to reference

a particular element of A.

The elements of A are denoted with a lowercase A and two numbers indicating their respective element

position in terms of row and column.

For instance a J is the element at position.

I j where i is the respective row and J is the respective column.

Therefore if we want to fill in the matrix it would start from a 1 1 then a 1 to a 1 3 until a 1 and

to finish the first row.

Similarly we’ve got a 1 1 8 2 1 8 3 1 until am 1 to complete the first column.

The last element of the matrix is a n a total number of elements is m times and.

OK great to finish off this introductory lecture.

We must note that in most programming languages albeit not all of them arrays start from zero rather

than one in Python for instance arrays start from zero.

So keep that in mind when coding all right.

In our next lecture we will look into vectors.

Thanks for watching.

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