Original subtitles

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Hello everyone and welcome to the lecture on our matrix exercise solutions.

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Walk through in this lecture video.

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I'm going to be going over the solutions for the Art Matrix exercises and explaining as we go along

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.

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Let's jump to our studio and get started.

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OK.

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So here we are our studio.

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I want to hit him just showing the scripting and the cons. windows.

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The first question or exercise we had to perform was to create two vectors and B were A's 1 2 3 and

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B is 4 5 6.

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Those vectors we had to use the C binder are Byne functions create a two by three Matrix from the vectors

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and we'll need to figure out which of these binding functions is the correct choice.

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Let's go ahead and get started.

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Well go ahead and assign a and we use the combined function that's the lowercase c and we'll do a similar

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process for creating B 4 5 6.

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And then what we had to do is figure out whether to use C bind or bind.

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So what's the actual difference here number that see Byne will bind columns together.

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So if we did see binds we would have a result that is a three by two Matrix and the instructions asked

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for a two by three.

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I mean the correct answer was to use our bind AB.

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And here we have our matrix.

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Let's go ahead and move on to exercise.

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Question number two.

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Exercise 2 was to create a three by three matrix consisting of the numbers 1 through 9.

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We had to create this met matrix using the shortcut.

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One call and nine is by specifying the n row argument in the matrix function call.

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Let's assign this matrix the variable M-80.

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Matt when you go ahead and clear the con..

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So just a quick reminder of what the actual shortcut looks like.

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This one Colan nine that creates a sequence of integers.

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So for example instead of having to write the combined function one two three for a continuous sequence

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of integers I can just say one colon three.

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And the syntax is your starting integer colon to your ending last in the integer.

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So how do we actually use this with the Matrix call or we're going to say matrix function will pass

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in one call in nine and then we're going to say by RHO equals true and we'll say number of rows is equal

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to 3.

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In order to have it be a three by three it's go to check to make sure that looks correct.

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One two three four five six seven eight nine.

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Everything's looking good.

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Let's go in and save that to the variable M-80.

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So I'll take that same command and I will sign it to the variable Max.

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And that's how we answer that question.

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A quick note.

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If you didn't specify by rote the equal true that's OK as well.

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So if he did something like this and ran that that would give you filled out by the columns which is

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also an acceptable answer doesn't really matter.

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You don't do by RHO true since it wasn't specified for this particular question.

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Let's go ahead and move on to the next question.

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All right.

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Question number three was to confirm that M-80 variable is a matrix.

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Using is dot matrix.

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Let me go and explain how that is that Matrix actually works.

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I'm going to say is dots.

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And you'll notice our studio will actually have a huge drop down menu of all the things we can check

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.

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So the is the methods are really useful if you're trying to check what data type data structure you're

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working with.

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Then in this case we're going to go ahead and check if something is a matrix.

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So you end up doing is say is that matrix and you pass in the variable you want to check and it'll return

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true because the M-80 variable is a matrix and you can actually use the same sort of operation for any

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data type.

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So if I go in and clear the console and say Is dots we can check if something is an array.

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So we can go ahead and pass in MIT and we get true in this case because Matrix's do count as a form

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of an array.

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Notice an array is not the same as a vector.

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You can think of a matrix as just a two dimensional array.

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But if we do something like check is dot for instance data frame which will learn about in more detail

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later we pass and met we get false because a matrix and a data frame aren't the same thing.

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Let's go ahead and move on to the next question.

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Number four exercise for was to create a five by five matrix consisting of the numbers 1 through 25

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and assign it to the variable M-80 2 and the top row should be the numbers 1 through 5.

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So we're going to do this really Similarly it's how we just did the last Matrix.

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I'm going to go ahead and say Matt 2 for my variable name and then I will pass in the matrix function

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.

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I'll use that shortcut to quickly create a vector one through 325.

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Notice it said the top row should be the numbers 1 through 5 meaning I want to fill this out by rows

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not by columns.

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So since my columns is the default meaning by rows is false.

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And I go ahead and say by row capital-T for true.

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And then finally I want this to be a five by five matrix.

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So I want the number of rows to be five.

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Let's go ahead and check that too.

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It looks like everything worked well.

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We have a five by five Matrix and we have one two three four five.

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OK moving on to the next question using indexing notation.

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Grab a subsection of Matt 2 from the previous exercise that looks like this 7 comma 8 12 comma 13.

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All right let's go ahead and do that.

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So let's go in and locate where 7 8 12 13 would be in or M8 to are meant to object.

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Looks like it's 78 right here in columns 2 and 3 wrote 2.

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And then we also have in the same columns 2 and 3 but row 3 total 13.

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So essentially want to grab this square chunk out of our matrix.

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Let's go ahead and do that well you use bracket notation.

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Or the indexing notation that we learned earlier.

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First thing I want to do is pass in the rows that I want in this case I want rows two through three

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.

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So one way I can do that is just by using that colon rotation rows two three three and actually want

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this exact same columns.

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So say comma exactly mutation and if I run that we get that result 7 8 12 13 to enter two times it goes

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up a bit.

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But here it is.

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So this is the correct way that index for that.

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Let's move on to the next exercise which is also an index notation exercise and for this exercise we

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want it to again grab a subsection that now looks like this 19 20 and 24 25.

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Looking again at our math to object we have 19 20 and 24 25 looks like that's a two by two subsection

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in rows and columns 4 5 and 4 5.

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So how do we do this.

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Well again it's going to be really similar.

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Hopefully if he did the last one you'll be able to answer this one as well.

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We're going in clear the councils we have in a Froom.

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I'll say I'm at 2 again so you can see it.

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I want 19 20 and 24 25.

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So again pass met to a pass in the rows that I want which is rows 4 through 5.

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And then I pass the columns I want which again is Aurthur 5.

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And there we have that subsection in the matrix.

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As mentioned during the matrix lectures it's really useful if you're struggling with this concept of

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rows common columns to just in your mind grab subsections of the matrix and then try to index them.

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So do a quick example of this.

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In case you're struggling this concept let's say I wanted to grab seven eight nine ten and then 12 13

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14 15.

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So a rectangular Matrix.

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Well I just identify the rows that I want so two three and it passes into Colon three and then identify

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the columns I want which is two three four five.

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So let's to call in five and I get this answer as a result.

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Again that's not an actual exercise question in this case.

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Just an example of how you can break this problem down.

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So if you're struggling with this make sure you practice it a lot just by choosing subsections and trying

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to get them out.

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Let's go to move on to the next exercise which was exercise 7.

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The question was What is the sum of all the elements in Mat 2.

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How do we actually do that.

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Well you can clear the console and we just use the sum function so we can say some math too.

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So hopefully to discover that if you just say some math to it will sum all the elements.

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Quick side note if you're looking to some just the columns or just the rows you can add additional arguments

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like call some's or sum up the column so we can go in and say I met two and then row sums.

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Works for the rows.

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All right.

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So those are just quick side notes.

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But in this case if you want to do all the elements shust normal some moving on we have one more exercise

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.

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And it was this.

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Find out how to use run I if this function to create a four by five matrix consisting of 20 random numbers

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four times five is equal to 20.

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All right let's go ahead and see how he would do this.

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First thing I'm going to assume that you've never actually seen this function before run.

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So I want to find out how to use it.

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Meaning I want to help on this.

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I'll say help.

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And pasan.

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Ron I-F and then boom we have a nice help tab here and we see what the arguments look like and what

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we should actually do.

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So what actually is run I.

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Well it's a uniform distribution.

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And what that means is these functions essentially provide information with the uniform distribution

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from the interval from min to Max.

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So how do we actually do this.

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We look here and notice we have a few uniform distribution functions.

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But the last one here is run.

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The one we referred to is a little small so hopefully you can call as far as font size.

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You can call help here and that spoiler's yourself.

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But if I just go in and copy this so we can see what it's actually saying in the documentation it says

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run a f n comma min equals zero Max equals 1.

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So those are the parameters or arguments we have to pass into this function and if we check out the

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documentation for what it is it says and is a number of observations.

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All right so we know we want 20 random numbers.

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So that means I want to draw 20.

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If I go yes go ahead and say run I if I pass in 20 and looks like it returns a vector of 20 random numbers

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.

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Perfect.

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Now I can also specify min and max value.

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So for instance right now I'm just doing random numbers.

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Frean the defaults and the defaults were 0 and 1.

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But if I go ahead and say run I if it's a random uniform distribution pass in 20 values I can also specify

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what I want the min value to be and the Max might be.

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So if I wanted to pick numbers tween 0 and 100 I could say many equals zero.

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And I could change my max to be 100.

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And now I get 25 or 20 random numbers between 0 and 100 in the solutions notebook I show putting in

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the men and the max.

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You don't actually have to do that.

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You could have just run run f 20.

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Let's go ahead and go with min and max settings.

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So how do we actually perform this.

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As far as creating this matrix of a four by five consisting of these when he ran the numbers will you

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just say matrix and then we pass in run I f 20

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and we wants four rows who want a four by five matrix and there is our matrix.

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And notice here even though it's printing out like this is a four by five.

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I'm going to go ahead and do is expand the window a bit.

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You can always check by what the index locations are the dimensions of your matrix.

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But if I run this again then we can see for sure that it's a four by five matrix.

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All right mixture of the notebook in case you're confused on anything but remember the main point of

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this last question was to get you used to reading help on functions that you don't know about and learning

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how to use them.

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All right.

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Hopefully that wasn't too bad.

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Make sure review the matrix lectures in case you're unsure of anything we just covered.

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Thanks and I'll see you at the next lecture