00:04
A be a n cross end matrix.
00:11
Here we need to prove that row vector of a are linearly dependent if and only if column vector of a linearly dependent.
00:56
So here we will prove this by using an example.
01:00
So here let a is a matrix of the form 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3 matrix.
01:17
So here we are taking a 3 cross 3 matrix where we have taken a first condition, that is, we have let, row vector are linearly dependent, and here, here, we need to prove column vector are linearly dependent.
01:52
So now considering this matrix a, we see that a is being taken as 1, 2, 3, 1, 2, 3, 1, 3, so here, a in which row vector are linearly dependent.
02:13
So here when we apply the row operation as, so here when we apply these two operations in this matrix say, it will be written as 1 -1 -1 -1 -1 -1.
02:27
So here clearly we can say that we are coming with a conclusion that column vector are linearly dependent...