00:01
Hello everyone so let's look into this question so we have the systematic question and we have to put it in a matrix form that is a x plus b a x plus b so a is going to be the coefficient of x y and z in the matrix form so this is going to be 3 0 and 2 this is minus 2 minus 2 and 1 this is minus 1 1 and 4 and x is x y z x y z and b is going to be the constant terms 4, 2 and 1 in this case so in the next part we have to calculate a inverse inverse matrix so here we have to calculate a inverse matrix so the we will use elimination method to calculate the inverse method so we write down the augmented matrix so augmented matrix is going to be 3, 0, 2, minus 2, minus 2, 1, minus 1, 1 and 4.
01:15
We will have here 1 0 0 0 0 0 0 1.
01:21
So we will go.
01:23
So we have to, what we will do, we first have to make this matrix into this form.
01:33
Like we have to have here has one one and one and all other terms should be zero so let's begin with the first term so divide the row first row with three okay so we will have one minus two by three minus one by three zero minus two one two one four so this is going to be one by three zero zero one zero zero zero zero zero zero zero zero one okay now we will multiply the row 1 by 2 in this case because we have to solve further we have to remove this part in this question so we have we are going to multiply r2 with we are going to r1 goes to 2 r1 so in this case we are going to have 2 minus 4 by 3 minus 2 by 3 0 minus 2 1 1 2 1 1 2 1 4 so this is going to be 2 by 3 0 01001 0 0 0 0 0 1 okay so the next subtract first row from the third row so this is what r3 goes to r3 minus r1 so this is going to be 2 and also r1 after the perform after performing this our first operation we are going to change all so r1 goes to r1 by 2 so in this case r1 by 2 so here 2 will change to this is going to be 1 minus 2 by 3 and this is going to be minus 1 by 3 this is 0 minus 2 and this is 1 so here we will have 0 7 by 3 14 by 3 and augmented matrix in this case will be 1 by 3 is 0 0 0 010 this is minus 2 by 3 0 and 1.
03:43
So the next we have to change these 2 1.
03:49
So what we will do? so make the point in the second column by dividing the 2 row by minus 2.
03:55
So we are going to divide the second row by minus 2.
03:58
So we will have 1 minus 2 by 3, minus 1 by 3, 0.
04:04
This will be 1.
04:05
This is minus 1 by 2.
04:07
0 7 by 3 7 by 3 14 by 3 and this will be 1 by 3 0 minus 2 by 3 0 this will be 1 by 2 minus 0 and 1 all right so now when we will move on to the 1 multiply the 2 row by minus 2 by 3.
04:38
So we will again multiply second row with the minus 2 by 3...