1. Consider the following system of linear equations 10x1 +...

1. Consider the following system of linear equations 10x1 + 7x2 + 8x3 + 7x4 = 32 7x1 + 5x2 + 6x3 + 5x4 = 23 8x1 + 6x2 + 10x3 + 9x4 = 33 7x1 + 5x2 + 9x3 + 10x4 = 31 a) Solve this system using Gauss elimination method. [4 marks] b) Replace the right hand side of the given system with (32.1, 22.9, 32.9, 31.1) and solve it. [4 marks] c) Comment on the stability of the system. [3 marks]

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00:01 So, let us start with the concept which we are going to use here for this question.

00:06 So, we are going to use the gauss elimination method to solve the given linear equations.

00:14 So, first of all let us write down the given system of linear equation that is 10x1 plus 7x2 plus 8 of x3 plus 7 of x4 is equals to 32.

00:28 Second equation is 7x1 plus 5x2 plus 6x3 plus 5x4 is equals to the 23.

00:40 Third is given 8x1 plus 6x2 plus 10x3 plus 9x4 is equals to the 33.

00:52 And the fourth one is 7 of x1 plus 5x2 plus 9x3 plus 10x4 is equals to the 31.

01:04 So, we have to solve these equations by the gauss elimination method.

01:09 So, for that we have to make a matrix form.

01:13 So, let's write down the matrix form here.

01:15 So, it will be simply 10 7 8 7 then 7 5 6 5 then 8 6 10 9 then 7 5 9 10.

01:29 Okay.

01:32 And the partition will be there.

01:33 So, let's say we do the partition here with their corresponding values of 32 then 23 33 and 31.

01:44 So, this will be the required matrix and by using elimination we just have to solve.

01:49 So, first we will apply the operation r1 divided by 10 tends to the r1.

01:57 Okay.

01:57 So, in that case our matrix will become the 1 0 .7 0 .8 0 .7 and here 32 by 10 will be 3 .2...

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