Solve, X.

[lvl107]

Hello, Everyone.

Thanks in advance for the time and help.

Best Regards.

[AlanStevens]

The determinant of the matrix multiplying the vector of (x, y, z) is zero.

An nxn nonhomogeneous system of linear equations has a unique non-trivial solution if and only if its determinant is non-zero. If the determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.

Alan

[lvl107]

Thanks for your response. I agree with you, Alan. And I'm also observing those ( for example ) :

Best Regards.

[Werner_E]

Something like this?

[Werner_E · Accepted solution]

??Absolutely not sure what the question is. What should X be? Ther term for x from the first example??

As Alan pointed out, the second system will not have a unique solution. If it has no solution at all or an infinite number of solutions depends on the rank of the extended matrix. If its 3, we will have no solution, if its 2 there is an infinite number of solutions. The latter case is for X=(sqrt(2)-1)*(a+b).

Mathcads result is inaccurate and misleading, but MC can do better using "fully":