00:01
In this problem, we have been given a matrix, let me name it a, it is 4, 1, 2 and 3, 1, 2 and 6, 2, 5.
00:20
And we have to find here, find here a inverse, means inverse of this matrix.
00:27
So, this is our question here.
00:29
So, to solve this problem, to solve it, let me use, let us use the formula, the formula, formula that is, here, formula that is a inverse is equal to adjoint of a, adjoint of a upon determinant of a.
01:00
So, we are going to use this formula.
01:04
So, let us first find the determinant of a.
01:07
So, we have given matrix a is equal to 4, 1, 2, 3, 1, 2, 6, 2, 5.
01:16
Let me use a row operation here, that is r1 going to r1 minus r2.
01:24
We know that after doing any row operation or column operation, the matrices, matrix remain the same and no changes occurs here.
01:34
So, by this operation, we get this here.
01:39
Okay.
01:39
So, 6, 2, 5 here.
01:41
We can see that now it will be damn easy to solve this matrix now, to find its determinant, 3, 1, 2 and 6, 2, 5.
01:55
So, now, to find its determinant, what we have to do is taken this line over here.
02:05
So, we will multiply this to this and subtract by multiplying this to this.
02:11
So, we have now 1 into 5 into 1, 1 into 5 minus 2 into 2.
02:20
So, and rest two are 0.
02:23
So, we don't have to calculate them.
02:26
So, we get 1 into 1.
02:28
So, we have find here mod of a means determinant of a is 1.
02:34
So, one part of the question has been done.
02:38
Now, let us find the adjoint of a.
02:41
We know that the adjoint of a is nothing but the transpose of coefficient matrix.
02:48
So, it is let me name this coefficient matrix cm.
02:53
Cm is the coefficient matrix, coefficient matrix...