00:01
Hello students, let's solve the system of equation using gaussian elimination.
00:05
Given system of equation is 4x plus 12y minus 7z minus 20w equal to 20 and another is 3x plus 9y minus 5z minus 28w equal to 36.
00:20
We can start by simplifying the equation that is x plus 3y minus 7 by 4z minus 5w equal to 5 and another is x plus 3y minus 5 by 3z minus 28 by 3w equal to 12.
00:40
Now let's perform the gaussian elimination to solve for x, y and z.
00:47
So subtracting equation 2 from equation 1 will get minus 1 by 12z plus 23 by 12w equal to minus 7.
00:57
So z equal to 23 by 12 into w plus 84.
01:07
So now multiplying both side of equation by minus 12 to elimination the fraction will get this.
01:13
Now we have this equation and this equations.
01:18
Now adding equation 1 to 2 to eliminate we have minus 1 by 12z plus 23 by 12w plus z minus 23 by 12w equal to minus 7 plus 84.
01:35
So now we will get 0, 0, z equal to w will become 0 because 23, 12w minus 23, 12w will become 0.
01:52
Z will get 1 minus 1 by 12 equal to minus plus 77.
01:58
So z equal to 11 by 12 equal to 77 that is equal to z equal to 7 into 12...