Matrices

 

A matrix is a rectangular array of numbers, symbols, or expressions. Matrices are often used to represent linear transformations, and can be used to represent systems of linear equations.

Here is an example of a matrix:

[a b] [c d]

This is a 2x2 matrix, which means it has 2 rows and 2 columns. The elements of the matrix are a, b, c, and d.

You can perform various operations on matrices, such as addition, subtraction, and multiplication. Matrix multiplication is different from scalar multiplication, as it involves multiplying the elements of the matrices according to a set of rules.

Here is an example of matrix addition:

[a b] [e f] [a+e b+f] [c d] + [g h] = [c+g d+h]

And here is an example of matrix multiplication:

[a b] [e f] [(ae+bg) (af+bh)] [c d] x [g h] = [(ce+dg) (cf+dh)]

I hope this helps! Let me know if you have any questions.