Wednesday, 24 September 2008

How to do the 3 x 3 order determinant using Rule of Sarrus

It is very often that we come across the word determinant in matrices. Yes, they are related.

Matrix consists a set of numbers. That's it.
Determinant is a numerical value obtained throught the numbers within the matrix.

For a 3 x 3 matrix, how then do we extract the determinant?

One of the easiest method to obtain this number is throught the use of Rule of Sarrus.

Below I show the steps.

Determinant A = [(aei) + (bfg) + (cdh) ] - [ (gec) + (hfa) + (idb) ].


The important step lies with getting the first left 2 columns out to the right of the determinant.

After which, we do a downwards grouping and addition.
This is followed by upwards grouping with addition again.

Note, the last step is to SUBTRACT the two groups obtained above.

(By grouping, I mean to MULTIPLY the individual elements).

Common mistakes:
1) The grouping is done by "adding" instead of multiplying the elements.

2) The slanted operations (the 3 element-multiplication) are done by "adding" instead of multiplying the 3 elements.

3) The two big groups are "added" instead of subtracted".

Just bear in mind the 3 common mistakes above and you are on the way to a happy matrix student...


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