how can I know when to apply cramer's rule?

[annynickname]

Hi.

I don't have problem solving equations applying cramer's rule, however my problem is that I don't understand in what cases I can succesfully solve a system of equations aplying cramer's rule, could you please teach me please.
thank you.

 

[tkhunny]

I do not understand your question. Cramer's Rule is one acceptable method among many for solving systems of equations. You can use whatever method suits your fancy. Cramer's Rule is important because it does two things very quickly.

1) An initial determinant of zero (0) tells you the system does not have a unique solution.
2) Getting a non-zero initial determinant, you know there is a unique solution. Never underestimate the power of something that guarantees existence.

 

[annynickname]

Thank you tkhunny.

my question is how do you know if you can succesfully apply cramer's rule? my textbook says something about the determinant can not be zero, but how do you know the determinant of a system of equations? for example

x-2y +3z = -1
-2x+y-5z=1
3x+3y+4z=2

my textbook says that the determinant of this equation is 6, I don't understand how my textbook came up with that answer, I'd write what they did , but since I don't have a program to write this kind of things it would look a mess.

 

[stapel]

my textbook says something about the determinant can not be zero, but how do you know the determinant of a system of equations? for example

How on earth did your book get to Cramer's Rule without first having discussed determinants?!? :shock:

To learn about determinants and how to compute them, please study some of the many lessons available online. You might also want to discuss this with your instructor or academic advisor. This textbook is apparently astonishingly-poorly written, and your instructor, at the least, should have noticed this and provided supplemental instruction to correct this glaring error! :?

Eliz.