⇒ A matrix is an array of elements (which are usually numbers) set out in a pair of brackets

⇒ You can describe the size of a matrix using the numbers of rows and columns it contains

⇒ A square matrix is one where the numbers of rows and columns are the same

⇒ A zero matrix is one in which all of the elements are zero. The zero matrix is denoted by 0

⇒ An identity matrix is a square matrix in which the elements of the leading diagonal (starting top left) are all 1 and the remaining elements are one. Identity matrices are denoted by I_k where k describes the size. The 3 x 3 identity matrix is:

⇒ To add or subtract matrices, you add or subtract the corresponding elements in each matrix. You can only add or subtract matrices of the same size

• Notation: matrices which are the same size are said to be additively conformable

⇒ To multiply a matrix by a scalar, you multiply every element in the matrix by that scalar

⇒ Also see our notes on:

• Matrix Multiplication
• Determinants
• Inverting a 2 x 2 Matrix
• Inverting a 3 x 3 Matrix
• Solving Systems of Equations Using Matrices