

 What is a vector? [YOUTUBE 2:27] [TRANSCRIPT]
 What is a vector? Example [YOUTUBE 1:15] [TRANSCRIPT]



 When are two vectors equal? [YOUTUBE 2:02][TRANSCRIPT]
 When are two vectors equal? Example [YOUTUBE 2:26][TRANSCRIPT]



 How do you add two vectors? [YOUTUBE 1:34][TRANSCRIPT]
 How do you add two vectors? Example [YOUTUBE 1:48] [TRANSCRIPT]



 What is a null (or zero) vector? [YOUTUBE 1:12] [TRANSCRIPT]
 What is a unit vector? [YOUTUBE 1:30][TRANSCRIPT]
 What is a unit vector? Example [YOUTUBE 1:49] [TRANSCRIPT]



 How do you multiply a vector by a scalar? [YOUTUBE 1:18] [TRANSCRIPT]
 How do you multiply a vector by a scalar? Example [YOUTUBE 1:16] [TRANSCRIPT]



 What do you mean by linear combination of vectors? [YOUTUBE 1:44] [TRANSCRIPT]
 What do you mean by linear combination of vectors? Example [YOUTUBE 2:34][TRANSCRIPT]
 What do you mean by vectors being linearly independent? [YOUTUBE 2:28] [TRANSCRIPT]
 Are these vectors linearly independent? Example 1 [YOUTUBE 3:17] [TRANSCRIPT]
 Are these vectors linearly independent? Example 2 [YOUTUBE 9:13][TRANSCRIPT]



 What do you mean by rank of a set of vectors? [YOUTUBE 2:09] [TRANSCRIPT]
 Rank of a set of vectors: Example 1 [YOUTUBE 3:53] [TRANSCRIPT]
 Rank of a set of vectors: Example 2 [YOUTUBE 2:27] [TRANSCRIPT]



 Prove that if a set of vectors contains a null vector, the set of vectors is linearly dependent [YOUTUBE 2:29] [TRANSCRIPT]
 Prove that if a set of vectors is linearly independent, then a subset of it is also linearly independent [YOUTUBE 5:42][TRANSCRIPT]
 Prove that if a set of vectors is linearly dependent, then at least one vector can be written as a linear combination of others [YOUTUBE 4:06] [TRANSCRIPT]



 How can vectors be used to write simultaneous linear equations? [YOUTUBE 5:08] [TRANSCRIPT]
 How can vectors be used to write simultaneous linear equations? Example [YOUTUBE 3:13][TRANSCRIPT]



 What is the definition of the dot product of two vectors? [YOUTUBE 2:00] [TRANSCRIPT]
 Dot product of two vectors Example [YOUTUBE 1:41] [TRANSCRIPT]
