00:01
Hello everyone, we are given the matrix a is equal to 4 cross 5 matrix as shown in the screen and we are asked to find the special solution to ax is equal to 0 for each free variable.
00:15
The first thing to do for special solution is we need to find a ram and using which we will find the keyword elements.
00:23
So apart from the pivot elements, the rest are the free variables.
00:27
So let's find the ramp.
00:29
So this matrix a is equivalent to.
00:34
So a is given by 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 14 2 4 3 3 0 0 0 1 minus 1.
00:51
So now this matrix.
00:53
Now we are going to eliminate elements in.
01:03
The first column under first element.
01:20
So that is going to give me the matrix 1 2 1 2 1 0 0 1 minus 1 1 1 1 and 0 0 1 minus 1 1 and 0 0 1 minus 1 1 1 and 0 0 1 minus 1 minus 1 minus 1 minus 1 1.
01:43
So this matrix is equivalent to.
01:46
So now we are going to do the elimination elements in the third column under third element...