00:01
Now, in this problem, we are given with this matrix and we need to find that for what values of r and s, the rank for this matrix is 2.
00:12
So let name this matrix to be a.
00:16
So the rank of a should be 2 for what values of r and s.
00:21
This is what we have to find.
00:23
Now, to solve this, we will do some row operations and we will try to make 0 here, 0 here.
00:30
Okay.
00:30
So for that, what we can do, i can write that r1 changes to r1 plus half of r4.
00:46
And also one more operation i'm doing, r2 changes to r2 minus r4.
00:54
So this matrix becomes r1 plus half of r4.
01:00
So this is 1 here, this 3 remain as it is, this would become 0.
01:04
And r2 changes to r2 minus r4.
01:07
So this is 0 as it is.
01:08
This is r2 minus 2.
01:12
Now this would become 0 here and rest as it is.
01:15
0, s minus 11 and then r plus 2 and finally 0, 0, 2.
01:26
Now one more row operation i'm doing.
01:31
So r3, it changes to r3 minus r plus 2 divided by 2 times r4...