MATRIX RULE COPIED!

2x2 Determinant

If A = ab cd
|A| = ad - bc
Concept: Product of main diagonal minus product of other diagonal.

Matrix Mastery Guide

aij
Element

A single number inside the matrix. 'i' is the row and 'j' is the column index.

m × n
Order / Size

Defines the matrix dimensions. Always Row count first, then Column count.

|A|
Determinant

A scalar value that helps find the Inverse and check if a system has solutions.

I
Identity

The 'number 1' of matrices. Multiplying any matrix by I leaves it unchanged.

AT
Transpose

The operation of flipping a matrix over its diagonal (swapping rows and columns).

A-1
Inverse

A matrix that, when multiplied with the original, results in the Identity Matrix.

0
Null Matrix

A matrix where every single element is zero. Used as the additive identity.

k·A
Scalar Multi

Multiplying the entire matrix by a single number. Every element gets multiplied.

det=0
Singular

If the determinant is 0, the matrix has no inverse. It's called Singular.

Legacy of the Matrix 🔳

[A]

200 BC | ANCIENT CHINA

The text 'The Nine Chapters on the Mathematical Art' used a matrix-like method (Fangcheng) to solve systems of linear equations using counting rods on a board.

1850 AD | JAMES SYLVESTER

James Joseph Sylvester first coined the term "Matrix" (Latin for womb). He saw it as a place where 'determinants' could grow and be born from.

1858 AD | ARTHUR CAYLEY

Arthur Cayley published 'A Memoir on the Theory of Matrices', defining matrix addition, multiplication, and inverses as we know them today.

"Did you know? Without Matrix Algebra, modern 3D video games and CGI movies would be impossible, as matrices are used to calculate every single movement and rotation of 3D objects!"