00:01
Hello everyone, we have given a question related to matrix in which we have given a matrix of order 4 cross 4.
00:10
Let's say this metric is a matrix a and we have to find the inverse of this matrix by inversion algorithm.
00:20
In inversion algorithm we have to do one thing that we will take this matrix on our left hand side and an identity.
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Matrix on our right -in side.
00:32
And we will do one thing that we will apply elementary operation on both sides so that the matrix a will convert in identity matrix, right? and the same operation which will we apply on left side, we will apply the same operation on the right -hand side, right? and when a matrix a will convert in identity matrix, then the matrix i will convert in which matrix that matrix will be the inverse of the given matrix a let me proceed to our solution first of all we will take a matrix a on left and identity matrix of same order as a on right inside right so the element of matrix a are one zero zero zero one three zero zero zero zero 1350 1357 and the element of identity matrix will be 1 000 0100 010 and 0001 on a so that it will become this type of matrix and the same elementary operation will be apply on this matrix right then this matrix will convert in inverse of given matrix right so first of all you can see the first row is same as the first row of this matrix so we don't need to change any element of this row now we will have to convert this one to zero.
02:36
So which elementary operation will we use to convert this one to zero? we can subtract this one to this one it will become zero and this one to this one it will also become zero.
02:50
On the same way we will apply the operation r4 ches to r4 minus r3.
02:58
On applying this operation we will get zero here.
03:02
And here right and then we will apply r3 change to r3 minus r2 then we will get zero here and here and then we will apply r2 change to r2 minus r1 then we will get zero here right so on applying this operation on both side we will get on left side the element of first row are one zero zero zero and one one so first of one we will apply this operation on fourth row as r4 change to r4 minus r3 so each element of r4 will subtract it from the elements of r3 respectively then we will get 1 minus 1, 0, 3 minus 3, 0, 5 minus 5, 0 and 7 minus 0, 7.
04:04
Similarly, now we will apply the same operation on the right hand side, then we will get 0 minus 0, 0 minus 1, 0 minus 1, and 1 minus 0.
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1.
04:18
Now r3 change to r3 minus r2.
04:21
So 1 minus 1, 0.
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3 minus 3, 0, 5 minus 0, 5 and 0 minus 0.
04:32
Same here.
04:34
0 minus 0, 0 minus 1, minus 1, 0.
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0 minus 1.
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1.
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0 minus 0.
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0.
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0.
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0 minus 0.
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0.
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0.
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0.
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0...