Do you know how to find a determinant of a 3x3 mtrix? If so applying cramer's rule is quite easy, have a read.
Cramer's rule - Wikipedia, the free encyclopedia
Spoiler:
OK, I have this question here that says:
Using Cramer's rule, solve
2x-y=4
3x+y-z=10
y+z=3
I have no idea how to show my working on the board, but having gone through the working to the best of my ability I came up with the answer:
x=2.33 y=1.55 and z=0.11
I'm certain that I'm wrong, I checked using a math program, but I can't tell where I went wrong with my working.
Could I get a little help figuring out how to post my working, and then troubleshoot it?
Do you know how to find a determinant of a 3x3 mtrix? If so applying cramer's rule is quite easy, have a read.
Cramer's rule - Wikipedia, the free encyclopedia
Spoiler:
Go here:
Cramer's Rule
it gives an easy to follow method of solving almost the exact problem you have.
I have some familiarity with it but my book has a very poor explanation of the concept--I had to search the internet just to find out that I had to use alternating signs.
I did the working by expanding the determinants by their minors on the first row.
I will do the working again by using the main diagonal(?) method, and report the result.
I would like to try to "master"(to some degree) the minor method and fix my flawed working.
That said, how can I post said working?
I think I can use latex but I'm not sure how to make it look good.
Alrighty! Here is the working I used in its unabridged form:
I started my working by defining system of equations and Determinant :
Then I defined determinants , and :
:
:
:
I expanded the determinants by their minor elements, in this instance I expanded them all about their first row elements.
I used the following template to help me remember the signs I had to use:
:
Final value of
:
Final value of
:
Final value of
:
Final value of
(I can already see where this might be going wrong.
Interestingly enough, I find myself getting a totally different answer from the first one I worked out.)
In order to find out what the values of x, y and z are, I divided the values of their determinants by D:
Threrefore: x=3, y=-1, z=1.
I know that the solution for y is wrong but I can't see what I did wrong.
Thank you for your help so far!