Ok so we’ve cover matrix transpose and multiplication, we’re now going to get into determinants. I’ll spread this into multiple posts as we’ll be eventually dealing with recursive functions. Determinants are a crucial glue in matrix math which allow you to find the inverse, which is akin to the reciprocal.
With the a 2 x 2 matrix, the determinant is single function – once we deal 3 x 3 and greater sized matrices we essentially recursively break them down to 2 x 2 and pass the base function. For a 2 x 2 matrix:
A B
C D
All we need to do is multiply the first element of the first row by the last element of the last row (A*D), and first element of the last row by the last element of the first row (C * B). Then take these away from each other (AD) – (CD) to give us our determinant:
1 2
4 1
(1*1) = 1
(4*2) = 8
(1-8) = -7
= -7
We’ll dig into 3 x 3 matrices next and then onto recursive methods…
is the (AD) – (CD) meant to be (AD) – (CB)?
thanks!
i love your blog, it’s helped me with so many math assignments. you’re a lifesaver!