Finding determinants of a 3×3 matrix
CraigsMaths
Mathematics Teaching for Learning
Determinants, Engineering Maths B
August 8th, 2008 by admin
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It is fairly simple to memorise the formula for the determinant of a 2×2 matrix:
Here we look at a simple approach that aids memorising the formula for a 3×3 matrix called Sarrus’ rule which will give you the determinant of a 3×3 matrix.
Example
We will find the determinant of a 3×3 matrix:
Step 1
Write 2 copies of the matrix side by side:
Step 2
Sum the products of the terms in each diagonal which starts in the top row and ends on the bottom in a left to right direction.
The sum of the products is:
Step 3
Now sum the products using the diagonals starting from the bottom row.
Step 4
The determinant will be:
Hint: If you end up with 3 groups of 3 terms in each of the brackets then all is well.
October 3rd, 2008 at 2:52 am
I must confess that this is a sure easy and smart way of completing finding the determinant of a 3×3 matrix.
Thanks so much.
November 5th, 2008 at 7:40 pm
Glad it helped! I wish bigger matrices were that easy.