Ok now lets Talk about matrix environments. Matrix environments are very simple to understand and its just like an array environment. An array
environment is something like tabular environment and the difference between Array environment
and tabular environment which we already learnt is that array environment works inside a math environment
first let's start with array environment and I will show you the difference between
array and other matrix environments start the array environment and let's delete all this
and we start the math environment here and end the math environment
environment just like table at environment it takes an argument. Argument means we have
to tell her many columns let's say we have three columns and this columns are centre
align so therefore c and no let's put the entries first one and then the second ampersand
in the second entry in the ampersand and the third so end of the line to the first
row then Foour ampersand, five ampersand 6 end of second line 7 ampersand 8 & nine
and no this is end of our array environment so if we compile this it will show me this
type of result just like this like this one this is our simple array environment
you can put anything I mean you can put a whole formula in this you can put any square
root any fraction so let me put a fraction in this so \frac it and Lets say
any number 2 divided by 3 and Less put I square root here so For square root we can go to
here and take a square root from there and let me say the previous one is a square, a ^ 2
+ B ^ 2 plus b squared if I compile this know you can see how latex perfectly aligned
this formula and everything without changing any line spacing it has adjusted fraction
by reducing the size of the digits in the fraction and perfectly balance the metrics is here now
this is a tabular or a table like environment some people prefer this environment
over tabular environment when you are putting math formulas in this so it's up to you and you
can use this environment if you want to put these lines so it's really simple just put
vertical bar here and you will get all these lines available to you this I already explained
in tabular element the same thing applies in array environment and for horizontal lines you can
also put a horizontal line for example at the top to can put \hline and if you want
a horizontal line after every line you can do it like this \hline and then then again \hline
and if you want to put at the end we have to fist enter the end of the line
and then you can put \hline and this will be a full box full of horizontal and vertical
lines so just like that so this is your horizontal and vertical line if you want if you want anything
of them is up to you know what is a matrix environment if you look here these are matrix environments
and latex offers us 5 matrix environment which are named \pmatrix, lower case \pmatrix
Upper case \Bmatrix matrix, lowe case \bmatrix upper case Vmatrix and these five and Wildman basically
only differ in the type of parentheses around the Matrix otherwise there's no difference
so it's just because all these are required in mathematics most liked matrices
is in this type of square brackets but some also use this type of this brackets and values
for determinant type of matrices in linear algebra any other math courses you will find this
type of determinants and also these double line only differ in the name and the bracket they offer
otherwise there is no difference now how these matrices differ from array environment is that these matrix environment do not require these arguments
this number of columns up to 10 columns and you can change this counter and this comes in advanced topics
But the simple thing is you dont have to ad this c c c 10 times in matrix environment it automatically takes whatever columns you are you are making
so let's start with this environment for him so what I do it instead of array I write pmatrix
and then I don't put any of these arguments and Less a recurring matters we don't have
these horizontal line so just remove this you look really ugly in Madison wi I've learnt
so just leave this and then we are done with this with a simple just change the name and
you will get another pair of brackets and wife at compile days you got this pmatrix
no there's no difference in any of these if you want bmatrix this one you just change
this to be Matrix and he will get another type of bracket you will get another type
of it that's it so simple it's only the matter of me what type of meme you put in the program
will get the same type of my trip I think this is enough whatever The same type of magic
I think this is enough Matrix whatever you want you can use it no this is a statement
Statement an agreement of merit so this is nothing special you just use bmatrix and then
instead of all these it want to you put a underscore and then in calibrate s111 to the
position of the row and column so this is basically just offered for number for row
b matrix in this entry instead of and like any number anything you just put this bachelet
detox back slider doors and disabilities redox so no need to explain anything I think this
is enough on my Flickr environments and no we have done all the equation environment
most of the dynasty few more equation environments available but with these splitter line and
kisses environmentally quirky Grande Ariana question environment you can write each and
every type of equation possible in mathematics I hope that you will be confident in you all
these equations and mattresses