Learning Objectives:

__Math Tutoring on Introduction to Matrices__

A** ****Matrix**** **is a rectangular arrangement or array of numbers in rows and columns often called **elements**. The plural of matrix is **Matrices**. The** ****Size **or** Dimension (m x n)** of a **matrix** identifies the number of **rows** as **m** and the number of **columns** is **n**. A **matrix** having only **one row **is called a** Row Matrix** and the matrix having **one column** is called a** Column Matrix**.

A **matrix** in which the number of rows is equal to the number of columns is called a** Square Matrix**.

A **square matrix** is called a **Diagonal Matrix** if no diagonal entries are all zero, the main diagonal can be constants or zeros.

A **square matrix** in which every diagonal element is** 1** and every no diagonal element is **0** is called an **Identity Matrix** or a **Unit Matrix**. A **matrix** in which every element is **0**, is called a **Zero** or **Null Matrix**.

Two **matrices** are** equal** if they have the same dimension and their corresponding elements are equal.

The **Transpose** of an **(n x m) matrix A **is an** (m x n) matrix** written as **A ^{T}**.

There are two ways to form the **transpose **of a** matrix: **

1) Write the **rows **of** A **as the** columns **of** A ^{T}.**

2) Write the **columns of A **as the** rows **of** A ^{T}. **

If** A = [a _{ij}] **then

If **A = A ^{T}** then

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**Hook Questions:**

*1. **In (m x p) matrix, between m & p which one represents the row and which one column?*

*2. **How to convert Augmented Matrix to Row Echelon form?*

*3. **What is Diagonal Matrix?*

*4. **How to obtain Transpose of a matrix?*

*5. **How to find free variables from a given matrix?*

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