Intro to Matrices — Transcript

Full transcript

1. 0:00in this video we're going to focus on
2. 0:02matrices
3. 0:05now what exactly is a matrix
4. 0:07a matrix is simply an array of numbers
5. 0:10organized into
6. 0:11rows and columns
7. 0:13and first let's talk about the order of
8. 0:15a matrix
9. 0:16so consider matrix a
10. 0:19and let's say
11. 0:20it has the numbers
12. 0:222 7
13. 0:24negative 4 6
14. 0:273 and 5.
15. 0:29what is the order of this matrix
16. 0:35now this matrix has
17. 0:37two rows
18. 0:40and three columns
19. 0:47now the rows are horizontal so this is
20. 0:49the first row
21. 0:51and this is the second row
22. 0:53the columns are vertical
23. 0:55this is the first column second
24. 0:58third
25. 1:00so there's two rows and three columns
26. 1:03so this is considered
27. 1:04a two by three matrix
28. 1:08the order of the matrix
29. 1:11list the rows first and then the number
30. 1:13of columns
31. 1:16now you need to be able to identify a
32. 1:19specific element
33. 1:20in a matrix for example
34. 1:23what is
35. 1:24element
36. 1:262 comma 3
37. 1:28or sometimes it can be written as just
38. 1:30element a23
39. 1:33so this is in matrix a
40. 1:36and
41. 1:37the first letter represents the row the
42. 1:40second letter is the column
43. 1:44so this is the first row this is the
44. 1:46second row
45. 1:47this is the first column second column
46. 1:49third column
47. 1:51so this element number five is in the
48. 1:54second row third column
49. 1:56so element a two three has a value of
50. 1:58five
51. 2:02now here's another one for you
52. 2:04what's element
53. 2:05a one two
54. 2:07and also element
55. 2:09a two one
56. 2:12go ahead and identify the value of these
57. 2:13elements
58. 2:15so element a one two that's in the first
59. 2:18row second column
60. 2:20so that has a value of seven element a21
61. 2:23is in the second row first column
62. 2:26and so that has a value of six
63. 2:30let's consider another matrix so let's
64. 2:32say if we have matrix b
65. 2:34and it has the numbers
66. 2:36four three
67. 2:37seven negative two
68. 2:40five six negative four
69. 2:42nine
70. 2:43negative three
71. 2:45eight
72. 2:46one
73. 2:47and negative seven
74. 2:49what is the order of the matrix
75. 2:53so let's start with the rows this is row
76. 2:55one
77. 2:56row two row three
78. 2:58and then the columns column one
79. 3:00two
80. 3:01three four
81. 3:04so the order of matrix b
82. 3:06it's a three
83. 3:09by four matrix
84. 3:11it has three rows and four columns
85. 3:18now identify
86. 3:20elements
87. 3:22b11
88. 3:26b
89. 3:282 3
90. 3:31b14
91. 3:34and b
92. 3:37three four go ahead and identify these
93. 3:40four elements
94. 3:42so this one is in the first row first
95. 3:44column
96. 3:45so that has a value of four
97. 3:47element b two three
98. 3:50that is in the second row
99. 3:53third column
100. 3:55so that has a value of negative four
101. 3:59and then element b14 is in the first row
102. 4:03fourth column
103. 4:05so that's equal to negative two
104. 4:08and element b34 is in the third row
105. 4:11fourth column
106. 4:12so it has a value of negative seven
107. 4:15so you need to be able to determine
108. 4:18the order of the matrix
109. 4:20and the value of every or any element in
110. 4:23the matrix
111. 4:25so what i'm going to do at this point is
112. 4:26i'm going to give you a list of matrices
113. 4:28and i want you to identify the order of
114. 4:31each matrix
115. 4:33so let's say if we have matrix c
116. 4:35and it has the numbers 3
117. 4:37negative 5
118. 4:382
119. 4:39negative 1
120. 4:41and then we have matrix d
121. 4:44which contains the elements
122. 4:46four
123. 4:48five
124. 4:49negative two
125. 4:50seven
126. 4:51three and negative
127. 4:54six then we have matrix e
128. 4:57which contains one number which is eight
129. 5:01matrix f
130. 5:03it's going to have seven
131. 5:05four
132. 5:07negative five
133. 5:08and
134. 5:1011.
135. 5:13and let's say
136. 5:15matrix g
137. 5:19has the numbers 3 1 7
138. 5:222 six negative four
139. 5:25nine zero three
140. 5:29so identify
141. 5:30the order
142. 5:32of each matrix
143. 5:35go ahead and try that
144. 5:37let me just give you one more matrix h
145. 5:42which is going to be 2 1
146. 5:447
147. 5:45negative 3
148. 5:466 negative 2 5
149. 5:48and 4.
150. 5:51and also determine which of these
151. 5:52matrices
152. 5:54represents a square matrix
153. 5:56so let's start with matrix c
154. 6:00it has two rows and it has two columns
155. 6:03so therefore
156. 6:05it's a 2 by 2 matrix
157. 6:09now
158. 6:10this is a square matrix because
159. 6:12the number of rows and columns are the
160. 6:14same
161. 6:16in the square all sides are the same
162. 6:19now for matrix d
163. 6:21we have three rows
164. 6:23and two columns
165. 6:26so this is going to be considered a
166. 6:29three by two
167. 6:30matrix
168. 6:34so the order of the matrix is always
169. 6:35going to be
170. 6:36the number of rows times the number of
171. 6:38columns
172. 6:41now for matrix e it has one row
173. 6:45and one column
174. 6:47so because it only has one number it's a
175. 6:49one by one
176. 6:51matrix
177. 6:53now for h
178. 6:55there are two rows
179. 6:58and there's
180. 7:00four columns
181. 7:02so this is a two by four
182. 7:05matrix
183. 7:08and then for f
184. 7:09we have one row
185. 7:11and
186. 7:13there's four columns so that's a one by
187. 7:14four matrix
188. 7:17and finally the last one g that's
189. 7:19another square matrix
190. 7:21as we can see there's three rows
191. 7:23and it has three columns
192. 7:26so that's a three by three
193. 7:28matrix so now you know how to determine
194. 7:31the order of the matrix and you also
195. 7:33know how to
196. 7:34identify the elements within a matrix
197. 7:38now let's focus on adding
198. 7:40matrices
199. 7:42so let's say if we have matrix a
200. 7:44and it has the numbers 2 3
201. 7:475 negative 4
202. 7:49and we have matrix b
203. 7:52which is uh
204. 7:537
205. 7:554
206. 7:56negative 3 and
207. 7:595.
208. 8:00what is the sum
209. 8:02of matrix a and b
210. 8:05so if we add in those two matrices
211. 8:08all we need to do
212. 8:10is
213. 8:11add the corresponding elements
214. 8:13and by the way
215. 8:14if you have a two by two matrix
216. 8:17you can only add it to another two by
217. 8:19two matrix
218. 8:20the number of rows and columns must be
219. 8:22the same when adding matrices or
220. 8:24subtract the matrices as well
221. 8:27so the first element
222. 8:29the one in the first row first column
223. 8:32we need to add it
224. 8:33with uh
225. 8:34element b11 in the first row in the
226. 8:36first column they have to match
227. 8:39so this is going to be 2 plus 7
228. 8:42and then we need to add
229. 8:44these two
230. 8:46so in the first row second column is
231. 8:48going to be 3 plus 4
232. 8:50and then we're going to add those two
233. 8:51numbers
234. 8:54so that's going to be five
235. 8:56plus negative three
236. 8:59and these two numbers which are in the
237. 9:00second row second column
238. 9:02the result will remain in that position
239. 9:05second row second column
240. 9:08now two plus seven
241. 9:10is nine
242. 9:11three plus four
243. 9:13is seven
244. 9:14five plus negative three is two
245. 9:17negative four plus five is one
246. 9:20so this is the sum of matrix a and b
247. 9:24and that's a simple way to add two
248. 9:26matrices together
249. 9:27it's not very complicated
250. 9:34now let's say if you want to multiply
251. 9:37matrix a by four
252. 9:39what will you get
253. 9:41four times a all you need to do is
254. 9:43multiply every element by four
255. 9:46so it's going to be four times two
256. 9:48four times three
257. 9:51four times five
258. 9:53and four times negative four
259. 9:57so then 4a
260. 9:58is going to equal
261. 10:018
262. 10:0212
263. 10:0320
264. 10:04and negative 16.
265. 10:11so what about subtracting two matrices
266. 10:14let's subtract matrix a and b
267. 10:18so we're going to start with a and then
268. 10:20subtract it by b so it's going to be 2
269. 10:21minus 7
270. 10:233 minus 4
271. 10:255 minus
272. 10:26negative 3
273. 10:28and then negative 4 minus 5.
274. 10:32so a minus b that's going to be two
275. 10:34minus seven which is negative five
276. 10:36three minus four is negative one
277. 10:39five minus negative three or five plus
278. 10:41three that's eight
279. 10:42negative four minus five is negative
280. 10:44nine
281. 10:46and so that's the difference
282. 10:47between
283. 10:48the two matrices
284. 10:51and that's it for this video if you want
285. 10:53to find more videos on pre-cal
286. 10:55feel free to check the description
287. 10:56section of this video i'm gonna post
288. 10:58some links there so thanks again for
289. 11:00watching
290. 11:22you