5x1 2x2 3x3 1 4x1 x3 7x4 1 2x1 x2 7x3 x4 3 3x1 9x2 x3 2x4 2...

5x1 -2x2 + 3x3 = -1 4x1 + x3 + 7x4 = 1 2x1 -x2 -7x3 + x4 = 3 -3x1 + 9x2 +x3 -2x4 =2 initial values x1=2, x2=0, x3=6, x4=3 Solve the equation system with third iterations using by Gauss-Seidel method

Transcript

00:01 Hi, in this question we are given with the set of equation as 5 times x1 minus 2 times x2 plus 3 times x3 is equals to minus 1.

00:12 4 times x1 plus x3 plus 7 times x4 is equal to 1.

00:21 2 times x1 minus 6 2 minus 7 times x3 plus x4 is equal to 3.

00:31 And minus 3 times x1 plus 9 times x2 plus x3 minus 2 times x4 is equals to 2 and we are given with the initial values for x1 as equals to 2 x2 x2 as equals to 0 x3 as equals to 6 and x4 as equals to 3 now we need to solve this using gos seedle method for that we we'll first as the coefficients of the given system is not diagonally dominant.

01:07 So we will rearrange the equations and we write it as 7 times x4 plus 4 times x1 minus 0 times x2 plus x3 is equals to 1.

01:23 0 times x4 plus 5 times x1 minus 2 times x2 plus 3 times x3 is equals to minus 1 and minus 2 times x4 minus 3 times x1 plus 9 times x2 plus x3 is equals to 2 and next equation is x4 plus 2 times x1 minus x2 minus 7 times x3 is equal to 3 now we can write the results for x4 k plus 1 that will be equals to 1 by 7 times 1 minus 4 times x 1 k minus 0 times x 1 k minus 0 times x 2 k minus 0 times x2 k minus x3k and we can write the result for x1 k plus 1 that will be equals to 1 by 5 times minus 1 minus 0 times x4 k plus 1 plus 2 times x2 k minus 3 x3 k and further we can write the results for x2 k plus 1 that will be equals to 1 by 9 times 2 plus 2 times x4 k plus 1 plus here we can write for 3 x1 k plus 1 minus x3 k and we can write the result for x3 k as equals to 1 by minus 7 times 3 k plus 1 minus 2 times x 1 k plus 1 plus 1 plus x 2 times x 1 k plus x 2 plus x 2 plus x 2 plus x 2 k plus 1 now using the first initial guess as we are given with for x1 it is given 2 x2 it is given 0 x 3 it is given 6 and x 4 it is given 3 so using all these values we can write the result for x 4 1 and this will be equals to substituting all these values, we get 1 by 7 times 1 minus 4 times 2 minus 0 minus 6.

04:24 And solving this we get this to be equals to minus 1 .8571...

Question

5x1 -2x2 + 3x3 = -1 4x1 + x3 + 7x4 = 1 2x1 -x2 -7x3 + x4 = 3 -3x1 + 9x2 +x3 -2x4 =2 initial values x1=2, x2=0, x3=6, x4=3 Solve the equation system with third iterations using by Gauss-Seidel method

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