#### Introduction to Matrices

- A matrix is a rectangular array of numbers. The numbers in the array are called the entries of the matrix. The following are examples of matrices:

\left[\begin{array}{cc}-3 & 4 \\5 & 6\end{array}\right] \quad\left[\begin{array}{l}5 \\6 \\7\end{array}\right]\quad\left[\begin{array}{ccc}\sqrt{2} & \pi & 3 \\0 & 0 & 1 \\\sqrt{2} & 0 & \pi\end{array}\right] \quad[5]

- As you can see above, each matrix have a certain number of rows (horizontal lines) and columns (vertical lines). Together we call it the size, or dimension of a matrix. For the examples above, their sizes (in order) are:

2 x 2, 3 x 1, 3 x 3, 1 x 1

To summarise, we write a matrix’s size as (no. of rows) x (no. of columns).

- We denote a_{ij} as the entry of a matrix in row i and column j.