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These are the user uploaded subtitles that are being translated: 1 00:00:00,510 --> 00:00:04,700 Hello everyone and welcome to the lecture on our matrix exercise solutions. 2 00:00:04,710 --> 00:00:06,950 Walk through in this lecture video. 3 00:00:06,990 --> 00:00:11,760 I'm going to be going over the solutions for the Art Matrix exercises and explaining as we go along 4 00:00:11,780 --> 00:00:12,040 . 5 00:00:12,300 --> 00:00:14,530 Let's jump to our studio and get started. 6 00:00:14,940 --> 00:00:15,210 OK. 7 00:00:15,210 --> 00:00:16,810 So here we are our studio. 8 00:00:16,830 --> 00:00:21,210 I want to hit him just showing the scripting and the cons. windows. 9 00:00:21,210 --> 00:00:26,850 The first question or exercise we had to perform was to create two vectors and B were A's 1 2 3 and 10 00:00:26,850 --> 00:00:28,490 B is 4 5 6. 11 00:00:28,680 --> 00:00:34,440 Those vectors we had to use the C binder are Byne functions create a two by three Matrix from the vectors 12 00:00:34,940 --> 00:00:38,990 and we'll need to figure out which of these binding functions is the correct choice. 13 00:00:39,000 --> 00:00:41,900 Let's go ahead and get started. 14 00:00:42,030 --> 00:00:49,230 Well go ahead and assign a and we use the combined function that's the lowercase c and we'll do a similar 15 00:00:49,800 --> 00:00:53,700 process for creating B 4 5 6. 16 00:00:54,450 --> 00:00:59,240 And then what we had to do is figure out whether to use C bind or bind. 17 00:00:59,400 --> 00:01:04,400 So what's the actual difference here number that see Byne will bind columns together. 18 00:01:04,560 --> 00:01:12,090 So if we did see binds we would have a result that is a three by two Matrix and the instructions asked 19 00:01:12,090 --> 00:01:13,530 for a two by three. 20 00:01:13,630 --> 00:01:20,010 I mean the correct answer was to use our bind AB. 21 00:01:20,310 --> 00:01:23,000 And here we have our matrix. 22 00:01:23,100 --> 00:01:25,080 Let's go ahead and move on to exercise. 23 00:01:25,080 --> 00:01:27,290 Question number two. 24 00:01:27,600 --> 00:01:33,100 Exercise 2 was to create a three by three matrix consisting of the numbers 1 through 9. 25 00:01:33,240 --> 00:01:35,750 We had to create this met matrix using the shortcut. 26 00:01:35,810 --> 00:01:42,080 One call and nine is by specifying the n row argument in the matrix function call. 27 00:01:42,120 --> 00:01:44,630 Let's assign this matrix the variable M-80. 28 00:01:44,630 --> 00:01:47,520 Matt when you go ahead and clear the con.. 29 00:01:48,120 --> 00:01:51,390 So just a quick reminder of what the actual shortcut looks like. 30 00:01:51,390 --> 00:01:56,730 This one Colan nine that creates a sequence of integers. 31 00:01:56,730 --> 00:02:03,330 So for example instead of having to write the combined function one two three for a continuous sequence 32 00:02:03,330 --> 00:02:06,830 of integers I can just say one colon three. 33 00:02:06,900 --> 00:02:14,040 And the syntax is your starting integer colon to your ending last in the integer. 34 00:02:14,070 --> 00:02:21,840 So how do we actually use this with the Matrix call or we're going to say matrix function will pass 35 00:02:21,930 --> 00:02:32,070 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 36 00:02:32,070 --> 00:02:33,000 to 3. 37 00:02:33,180 --> 00:02:38,130 In order to have it be a three by three it's go to check to make sure that looks correct. 38 00:02:38,160 --> 00:02:40,430 One two three four five six seven eight nine. 39 00:02:40,620 --> 00:02:41,570 Everything's looking good. 40 00:02:41,580 --> 00:02:46,130 Let's go in and save that to the variable M-80. 41 00:02:46,130 --> 00:02:50,300 So I'll take that same command and I will sign it to the variable Max. 42 00:02:50,880 --> 00:02:53,160 And that's how we answer that question. 43 00:02:53,220 --> 00:02:53,900 A quick note. 44 00:02:53,940 --> 00:02:58,070 If you didn't specify by rote the equal true that's OK as well. 45 00:02:58,080 --> 00:03:06,180 So if he did something like this and ran that that would give you filled out by the columns which is 46 00:03:06,180 --> 00:03:09,270 also an acceptable answer doesn't really matter. 47 00:03:09,270 --> 00:03:13,890 You don't do by RHO true since it wasn't specified for this particular question. 48 00:03:13,920 --> 00:03:17,090 Let's go ahead and move on to the next question. 49 00:03:17,100 --> 00:03:17,430 All right. 50 00:03:17,430 --> 00:03:21,320 Question number three was to confirm that M-80 variable is a matrix. 51 00:03:21,360 --> 00:03:23,290 Using is dot matrix. 52 00:03:23,340 --> 00:03:27,910 Let me go and explain how that is that Matrix actually works. 53 00:03:28,050 --> 00:03:29,420 I'm going to say is dots. 54 00:03:29,490 --> 00:03:35,160 And you'll notice our studio will actually have a huge drop down menu of all the things we can check 55 00:03:35,180 --> 00:03:35,450 . 56 00:03:35,670 --> 00:03:41,220 So the is the methods are really useful if you're trying to check what data type data structure you're 57 00:03:41,220 --> 00:03:42,140 working with. 58 00:03:42,210 --> 00:03:45,670 Then in this case we're going to go ahead and check if something is a matrix. 59 00:03:45,870 --> 00:03:52,320 So you end up doing is say is that matrix and you pass in the variable you want to check and it'll return 60 00:03:52,320 --> 00:04:00,720 true because the M-80 variable is a matrix and you can actually use the same sort of operation for any 61 00:04:00,720 --> 00:04:01,360 data type. 62 00:04:01,350 --> 00:04:06,780 So if I go in and clear the console and say Is dots we can check if something is an array. 63 00:04:06,960 --> 00:04:14,400 So we can go ahead and pass in MIT and we get true in this case because Matrix's do count as a form 64 00:04:14,400 --> 00:04:15,720 of an array. 65 00:04:15,730 --> 00:04:17,960 Notice an array is not the same as a vector. 66 00:04:18,180 --> 00:04:20,860 You can think of a matrix as just a two dimensional array. 67 00:04:21,030 --> 00:04:28,590 But if we do something like check is dot for instance data frame which will learn about in more detail 68 00:04:28,590 --> 00:04:34,640 later we pass and met we get false because a matrix and a data frame aren't the same thing. 69 00:04:34,650 --> 00:04:38,710 Let's go ahead and move on to the next question. 70 00:04:38,710 --> 00:04:44,460 Number four exercise for was to create a five by five matrix consisting of the numbers 1 through 25 71 00:04:44,820 --> 00:04:50,090 and assign it to the variable M-80 2 and the top row should be the numbers 1 through 5. 72 00:04:50,400 --> 00:04:54,690 So we're going to do this really Similarly it's how we just did the last Matrix. 73 00:04:54,690 --> 00:05:01,200 I'm going to go ahead and say Matt 2 for my variable name and then I will pass in the matrix function 74 00:05:01,200 --> 00:05:01,790 . 75 00:05:02,090 --> 00:05:07,730 I'll use that shortcut to quickly create a vector one through 325. 76 00:05:07,740 --> 00:05:12,900 Notice it said the top row should be the numbers 1 through 5 meaning I want to fill this out by rows 77 00:05:12,900 --> 00:05:14,140 not by columns. 78 00:05:14,160 --> 00:05:18,200 So since my columns is the default meaning by rows is false. 79 00:05:18,210 --> 00:05:22,920 And I go ahead and say by row capital-T for true. 80 00:05:23,120 --> 00:05:26,370 And then finally I want this to be a five by five matrix. 81 00:05:26,370 --> 00:05:29,150 So I want the number of rows to be five. 82 00:05:29,610 --> 00:05:31,790 Let's go ahead and check that too. 83 00:05:32,490 --> 00:05:33,840 It looks like everything worked well. 84 00:05:33,840 --> 00:05:37,940 We have a five by five Matrix and we have one two three four five. 85 00:05:38,520 --> 00:05:42,420 OK moving on to the next question using indexing notation. 86 00:05:42,450 --> 00:05:50,370 Grab a subsection of Matt 2 from the previous exercise that looks like this 7 comma 8 12 comma 13. 87 00:05:50,370 --> 00:05:52,390 All right let's go ahead and do that. 88 00:05:52,710 --> 00:05:58,830 So let's go in and locate where 7 8 12 13 would be in or M8 to are meant to object. 89 00:05:58,830 --> 00:06:03,510 Looks like it's 78 right here in columns 2 and 3 wrote 2. 90 00:06:03,810 --> 00:06:08,530 And then we also have in the same columns 2 and 3 but row 3 total 13. 91 00:06:08,700 --> 00:06:12,480 So essentially want to grab this square chunk out of our matrix. 92 00:06:12,780 --> 00:06:16,020 Let's go ahead and do that well you use bracket notation. 93 00:06:16,020 --> 00:06:18,750 Or the indexing notation that we learned earlier. 94 00:06:18,750 --> 00:06:25,500 First thing I want to do is pass in the rows that I want in this case I want rows two through three 95 00:06:25,500 --> 00:06:26,290 . 96 00:06:26,490 --> 00:06:32,850 So one way I can do that is just by using that colon rotation rows two three three and actually want 97 00:06:32,850 --> 00:06:34,360 this exact same columns. 98 00:06:34,450 --> 00:06:42,750 So say comma exactly mutation and if I run that we get that result 7 8 12 13 to enter two times it goes 99 00:06:42,750 --> 00:06:43,490 up a bit. 100 00:06:43,610 --> 00:06:45,210 But here it is. 101 00:06:45,210 --> 00:06:47,600 So this is the correct way that index for that. 102 00:06:48,090 --> 00:06:54,450 Let's move on to the next exercise which is also an index notation exercise and for this exercise we 103 00:06:54,450 --> 00:07:01,620 want it to again grab a subsection that now looks like this 19 20 and 24 25. 104 00:07:01,860 --> 00:07:10,140 Looking again at our math to object we have 19 20 and 24 25 looks like that's a two by two subsection 105 00:07:10,650 --> 00:07:14,470 in rows and columns 4 5 and 4 5. 106 00:07:14,910 --> 00:07:15,780 So how do we do this. 107 00:07:15,780 --> 00:07:17,510 Well again it's going to be really similar. 108 00:07:17,520 --> 00:07:21,190 Hopefully if he did the last one you'll be able to answer this one as well. 109 00:07:21,240 --> 00:07:24,000 We're going in clear the councils we have in a Froom. 110 00:07:24,120 --> 00:07:27,010 I'll say I'm at 2 again so you can see it. 111 00:07:27,330 --> 00:07:30,960 I want 19 20 and 24 25. 112 00:07:30,960 --> 00:07:38,280 So again pass met to a pass in the rows that I want which is rows 4 through 5. 113 00:07:38,640 --> 00:07:43,610 And then I pass the columns I want which again is Aurthur 5. 114 00:07:43,860 --> 00:07:47,280 And there we have that subsection in the matrix. 115 00:07:47,280 --> 00:07:52,200 As mentioned during the matrix lectures it's really useful if you're struggling with this concept of 116 00:07:52,560 --> 00:08:00,070 rows common columns to just in your mind grab subsections of the matrix and then try to index them. 117 00:08:00,360 --> 00:08:02,310 So do a quick example of this. 118 00:08:02,310 --> 00:08:08,190 In case you're struggling this concept let's say I wanted to grab seven eight nine ten and then 12 13 119 00:08:08,190 --> 00:08:08,940 14 15. 120 00:08:08,940 --> 00:08:10,580 So a rectangular Matrix. 121 00:08:10,830 --> 00:08:19,690 Well I just identify the rows that I want so two three and it passes into Colon three and then identify 122 00:08:19,710 --> 00:08:22,340 the columns I want which is two three four five. 123 00:08:22,350 --> 00:08:28,140 So let's to call in five and I get this answer as a result. 124 00:08:28,140 --> 00:08:30,420 Again that's not an actual exercise question in this case. 125 00:08:30,420 --> 00:08:33,530 Just an example of how you can break this problem down. 126 00:08:33,570 --> 00:08:38,970 So if you're struggling with this make sure you practice it a lot just by choosing subsections and trying 127 00:08:38,970 --> 00:08:40,130 to get them out. 128 00:08:40,620 --> 00:08:45,180 Let's go to move on to the next exercise which was exercise 7. 129 00:08:45,210 --> 00:08:49,400 The question was What is the sum of all the elements in Mat 2. 130 00:08:49,530 --> 00:08:50,930 How do we actually do that. 131 00:08:51,210 --> 00:08:59,960 Well you can clear the console and we just use the sum function so we can say some math too. 132 00:09:01,050 --> 00:09:06,210 So hopefully to discover that if you just say some math to it will sum all the elements. 133 00:09:06,240 --> 00:09:12,630 Quick side note if you're looking to some just the columns or just the rows you can add additional arguments 134 00:09:12,720 --> 00:09:21,840 like call some's or sum up the column so we can go in and say I met two and then row sums. 135 00:09:22,260 --> 00:09:24,520 Works for the rows. 136 00:09:24,660 --> 00:09:24,930 All right. 137 00:09:24,990 --> 00:09:26,360 So those are just quick side notes. 138 00:09:26,370 --> 00:09:33,330 But in this case if you want to do all the elements shust normal some moving on we have one more exercise 139 00:09:33,330 --> 00:09:34,380 . 140 00:09:34,380 --> 00:09:35,460 And it was this. 141 00:09:35,460 --> 00:09:43,320 Find out how to use run I if this function to create a four by five matrix consisting of 20 random numbers 142 00:09:43,920 --> 00:09:46,350 four times five is equal to 20. 143 00:09:46,350 --> 00:09:49,400 All right let's go ahead and see how he would do this. 144 00:09:49,470 --> 00:09:53,610 First thing I'm going to assume that you've never actually seen this function before run. 145 00:09:53,900 --> 00:09:55,260 So I want to find out how to use it. 146 00:09:55,290 --> 00:09:56,970 Meaning I want to help on this. 147 00:09:56,970 --> 00:09:58,010 I'll say help. 148 00:09:58,140 --> 00:09:58,960 And pasan. 149 00:09:59,010 --> 00:10:06,300 Ron I-F and then boom we have a nice help tab here and we see what the arguments look like and what 150 00:10:06,330 --> 00:10:07,170 we should actually do. 151 00:10:07,170 --> 00:10:09,320 So what actually is run I. 152 00:10:09,390 --> 00:10:11,400 Well it's a uniform distribution. 153 00:10:11,520 --> 00:10:15,780 And what that means is these functions essentially provide information with the uniform distribution 154 00:10:15,780 --> 00:10:19,020 from the interval from min to Max. 155 00:10:19,020 --> 00:10:21,250 So how do we actually do this. 156 00:10:21,270 --> 00:10:26,660 We look here and notice we have a few uniform distribution functions. 157 00:10:26,760 --> 00:10:28,390 But the last one here is run. 158 00:10:28,450 --> 00:10:33,030 The one we referred to is a little small so hopefully you can call as far as font size. 159 00:10:33,130 --> 00:10:35,250 You can call help here and that spoiler's yourself. 160 00:10:35,460 --> 00:10:41,430 But if I just go in and copy this so we can see what it's actually saying in the documentation it says 161 00:10:41,520 --> 00:10:45,660 run a f n comma min equals zero Max equals 1. 162 00:10:45,660 --> 00:10:49,800 So those are the parameters or arguments we have to pass into this function and if we check out the 163 00:10:49,800 --> 00:10:54,860 documentation for what it is it says and is a number of observations. 164 00:10:54,870 --> 00:10:58,160 All right so we know we want 20 random numbers. 165 00:10:58,320 --> 00:11:00,970 So that means I want to draw 20. 166 00:11:01,130 --> 00:11:11,410 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 167 00:11:11,400 --> 00:11:11,430 . 168 00:11:11,430 --> 00:11:13,040 Perfect. 169 00:11:13,110 --> 00:11:16,800 Now I can also specify min and max value. 170 00:11:17,220 --> 00:11:19,770 So for instance right now I'm just doing random numbers. 171 00:11:19,770 --> 00:11:23,420 Frean the defaults and the defaults were 0 and 1. 172 00:11:23,520 --> 00:11:34,200 But if I go ahead and say run I if it's a random uniform distribution pass in 20 values I can also specify 173 00:11:34,200 --> 00:11:36,710 what I want the min value to be and the Max might be. 174 00:11:36,720 --> 00:11:43,180 So if I wanted to pick numbers tween 0 and 100 I could say many equals zero. 175 00:11:43,470 --> 00:11:46,060 And I could change my max to be 100. 176 00:11:46,470 --> 00:11:55,410 And now I get 25 or 20 random numbers between 0 and 100 in the solutions notebook I show putting in 177 00:11:55,410 --> 00:11:56,660 the men and the max. 178 00:11:56,670 --> 00:11:57,840 You don't actually have to do that. 179 00:11:57,840 --> 00:12:00,920 You could have just run run f 20. 180 00:12:00,960 --> 00:12:05,190 Let's go ahead and go with min and max settings. 181 00:12:05,190 --> 00:12:06,750 So how do we actually perform this. 182 00:12:06,750 --> 00:12:11,100 As far as creating this matrix of a four by five consisting of these when he ran the numbers will you 183 00:12:11,100 --> 00:12:17,820 just say matrix and then we pass in run I f 20 184 00:12:20,490 --> 00:12:28,990 and we wants four rows who want a four by five matrix and there is our matrix. 185 00:12:29,190 --> 00:12:33,670 And notice here even though it's printing out like this is a four by five. 186 00:12:33,830 --> 00:12:36,670 I'm going to go ahead and do is expand the window a bit. 187 00:12:36,720 --> 00:12:41,960 You can always check by what the index locations are the dimensions of your matrix. 188 00:12:41,970 --> 00:12:47,260 But if I run this again then we can see for sure that it's a four by five matrix. 189 00:12:47,310 --> 00:12:52,170 All right mixture of the notebook in case you're confused on anything but remember the main point of 190 00:12:52,170 --> 00:12:58,230 this last question was to get you used to reading help on functions that you don't know about and learning 191 00:12:58,230 --> 00:13:00,080 how to use them. 192 00:13:00,120 --> 00:13:00,980 All right. 193 00:13:01,140 --> 00:13:02,960 Hopefully that wasn't too bad. 194 00:13:02,970 --> 00:13:08,000 Make sure review the matrix lectures in case you're unsure of anything we just covered. 195 00:13:08,220 --> 00:13:09,750 Thanks and I'll see you at the next lecture 19652