00:01
Hello, welcome to this lesson.
00:03
In this lesson we are looking for the value of k in a vector 1, k negative 2 for which we have a linear combination of e1 which is 1, 2, 3 and e2 which is 2, 3 and 1.
00:22
All right, so the first thing that we'll do is that we look for scalars a and b such that we can have the vector 1, k and negative 2 represented as the scalar a times the first vector which is 1, 2 and 3 then plus the second vector which is 2, 3 and 1.
00:48
So if there is this scalars a and b such that we can write the vector 1, k negative 2 then actually we can have a value of k such that the vectors e1 and e2 can be written as a linear combination of the vector 1, k negative 2.
01:11
So here if we expand then we would have 1 that is equals to so a times 1 right which is a then 2 times b right which will be 2b so this will be equation 1.
01:38
Then when we go to the second part we have k which is equals to 2 times a times this value then we have 3 times this value so plus 3 b so this is equation 2.
01:55
Then we also have negative 2 which is equals to a times 3 so 3 a then b times 1 so this is plus b that is equals to equation 3...