2. Large Determinants
by M. Bourne
Evaluating large determinants can be tedious and we will use computers wherever possible (see box at right). But if you have to do large determinants on paper, here's how.
Computers and Determinants
Now that we have powerful tools like LiveMath, MathCad, Scientific Notebook, Mathematica, Matlab, Maple, etc, we should concentrate on understanding the uses of mathematics and not so much on its mechanics.
Students spend hours multiplying out large determinants and a lot of the time is spent figuring out where errors were made. And for what? That time is better spent using a computer (or calculator) to solve it directly for us and using the remaining time learning how to apply it.
Mostly, we will use LiveMath or other Computer Algebra Systems to find large determinants.
Expanding 4×4 Determinants
We will use the same approach that we saw in the last section, where we expanded a 3×3 determinant.
Going down the first column, we find the cofactors of each element and then multiply each element by its cofactor.
Notice the pattern of
First term: positive
Second term: negative
Third term: positive
Fourth term: negative
To get the final answer, we expand out these 3×3 determinants, multiply then simplify.
Example
Expand the 4×4 determinant:
As mentioned above, we will use computer to find the value of large determinants.
Here is how we use LiveMath to find the value of a 4×4 determinant.
Didn't find what you are looking for on this page? Try search:
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Algebra Lessons on DVD
Easy to understand algebra lessons on DVD. See samples before you commit.
More info: Algebra videos
Book mark this page
Add this page to Del.icio.us, Furl, Digg, StumbleUpon, Google, whatever...
Need a break? Play a math game. Well, they all involve math... No, really!
