00:01
In the question given matrix is in the first row the elements are that is 1, 2, 3.
00:09
In the second row elements are minus 2, 1 ,0 and in the third row the elements are 3 minus 1 1.
00:17
So this matrix is given in the cushion and i'm representing it by a.
00:24
Now in the question it is asking to find the inverse of given matrix.
00:27
Means i have to find out a inverse so for finding this my first step is i will write the given matrix in augmented matrix so as is no augmented matrix will be written as matrix on the left side i we have to write the given matrix means a and on the right side we have to write the multiplicative identity matrix means i and order will be same as given matrix order so i have to write this way so it means i can write augmented i i can write in the augmented matrix form that will be on the left side the elements are in the first row one two three in the second row minus two one zero and in the third row elements are 3 minus 1 1 and now on the right side the elements are as you see this is an identity matrix identity matrix so i can say that say that in the first row elements are 1 -0 in the second row elements are 010 and in the third row elements are 0 -0 1 now my next step is i will do some row and column operations to make this left side as a similar to right side means i am making this left side as the identity matrix means in i can say that i will convert in i so by doing operation that when i'm converting the left side then right side also changing so what i get in the result will be that will get that will be said as a inverse means inverse matrix so let's start by doing operations so first operation is that is row operation is first i will apply for second row and the operation is that is r2 plus 2 r1 so this is applying for only second row so it means in the first and in the third row the elements are written as same so in the first row the element will be see the above step augmented matrix so i can write the elements in the first row that is one two three and on the right side the elements are one zero zero now in the third row the elements are three minus one one and on the right side that is zero zero one now take a operation and write the elements in the second row so in the second row the new elements are after taking operation i can say that year zero year five year six and year two one zero so now next step is taking a operation for third row means operation is that is r3 minus three times of r1 and this operation is applying only for third row means r3 so it means in the first row and in the second row the elements are same so look the above elements matrix sorry and the elements are written as in the first row is 1, 2, 3 and on the right side it will return as 100 and in the second row the elements are 056 and on the right side that is 210.
04:30
Now in the third row the elements will be after this applying operation i can say that element will be here element will be that is r3 minus 3 r1 means 3 minus means i have to multiply minus three with the elements in the first row then add with element in the third row.
04:58
So what i get elements are that is here i will add zero then here minus seven, year minus eight and year will be written as minus three and year zero and year one.
05:15
So these are elements i get in which i get in the third row.
05:19
Now next operation is written as that is r2 divided by 5 means and this operation is applying only for second row it means in the second row the element elements is dividing by 5 so new elements in the second row will be look above again the augmented matrix this so i can say that in the second row the elements will be here i will write 0 here i will write 5 divided by means one here i will write six divided by five and on the right side here i will write that is two divided by five year one divided by five and this become zero now this operation is applying only for second row it means in the first row and in the third row the elements are same so in the first row the elements will be that is one two three and on the right side that is one zero zero and in the third row the elements will be zero minus seven minus eight and on the right side that is minus 301 now next operation is i will i will take a operation for first row so operation is that is r1 minus 2 r2 r1 minus 2 and this will applying only for first row so it means in the second row and in the third row the elements are eaten as same so look above this matrix so i can say in the second row and in the third row elements are so first in the second elements is 016 divided by 5 so these are on the left side and on the rights elements are 2 divided by 5 1 divided 5 and 0 and on the right side in the third row the elements are sorry left -side elements are 0 minus 7 minus 8 and now in the right side on the right side the elements are minus 3 0 1 now for first row i will take this operation and write the element.
07:37
So here i will write elements.
07:41
So look again of written operations.
07:44
So it says it will say that i have to multiply minus 2 with the elements in the second row and then add with the elements matching elements in the first row...