Gauss-Elimination Problems

I stuck with these 2 problems for a long time :( not sure that it is defined or not

Question 1: Give all solutions, if any, of

x + y =1

sin(x - y) =1/2

with 0 less than or equal to X and X is less than or equal to 3

Question 2: Give all solutions, if any, of

sinx +siny = -1

sinx - siny + 4cosz =1

sinx + siny + 2cosz =2

For this problem; after I did Gauss Ellimination, I got

[1 1 0 -1]

[0 1 -2 -1]

[0 0 1 3/2] Then z=3/2, y=2, x=-3

but siny=sin2=undefined and sinx=sin(-3)=undefined

I am not sure what I have done wrong, please help

Thank you

Re: Gauss-Elimination Problems

Re: Gauss-Elimination Problems

In Question 2, I believe you found the supposed values of sin(x), sin(y) and cos(z) correctly. Since sin(x) = -3 has no solutions, the original systems has no solutions, either.

For Question 1, express y through x from the first equation, substitute it into the second equation and use the fact that iff , or , . Select suitable values of x between 0 and 3.

Re: Gauss-Elimination Problems

Thank you emakorov,

I still dont get the question 1.

as you told me the next step should be

x + y = 1

sin(2x-1) =1/2 --> substitute eq1 in eq2

but I don't know what to do next?

[1 1 1]

[2 0 1/2] and so on?

Re: Gauss-Elimination Problems

Quote:

Originally Posted by

**angelme** sin(2x-1) =1/2 --> substitute eq1 in eq2

but I don't know what to do next?

[1 1 1]

[2 0 1/2] and so on?

Of course not. Gauss elimination procedure applies only to a system of linear equations, where unknown variables are multiplied by constants and added. The equation sin(2x-1) =1/2 is nonlinear because it involves a sine applied to an expression with x. I gave the relevant fact in post #3 (in this case, ).

Re: Gauss-Elimination Problems

Re: Gauss-Elimination Problems

Re: Gauss-Elimination Problems

Hello again, angelme!

From [2], we have: .

. . . . . . . . . .

. . . . . . . . . .

n . . . . . . . . .