## Blog

# Why Matrix is Used?

- September 22, 2018
- Posted by: allexamshelps
- Category: Mathematics Research Methodology

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54,925 total views, 34 views today

** Addition of N Matrices**

**Why Matrix is Used:**

**We study matrices because all real data comes in the form of a matrix.**

**Notice that the above figures are actually in the form of a matrix, and this is a 9x5 matrix where 9 (years) is the number of rows and the ****5 (variables) are the number of columns. All real data is available in this form (The year column is not data and hence ignored).**

**The above figure shows one more example of real data and it is also in the form of a matrix and it is a 5x6 matrix ****(again the year column is not data) where the number of years is the 5 rows and the components of the income statement ****are 6 columns. No matter, which subject (Science, Engineering, Social science, etc.) you study if you closely ****notice then you will find that all real data actually come in the form of a matrix. This is why we study matrix.**

**Even if you write a single digit, we read them as a scalar quantity like 2, 3, 4 etc. or all single real numbers are called scalar quantity and considered in matrix algebra.**

**A matrix is a rectangular array (arrangement) of numbers where the rows appear horizontally and the columns appear vertically.**

**The following is an example of a 2x3 matrix where the number of rows is 3 and the number of columns is 2.**

**A={ \begin{bmatrix} { Column }_{ 1 } & { Column }_{ 2 } \\ 2 & 1 \\ 3 & 7 \\ 3 & 5 \end{bmatrix} }_{ 3(Rows)\quad \times \quad (2)columns }**

**we first write the number of rows and then the number of columns. **

**All the data points of a matrix are called the elements of the matrix. **

**In symbolic form, we indicate an element in ****{ a }_{ ij } ****where we denote the number of row by 'i' and the column by 'j'.**

** ****{ a }_{ 11 } ****indicates the element in the first row and first column. **

**Similarly, ****{ a }_{ 32 } ****indicates the element in the first row and second column.**

#### Ex. **{ a }_{ 11 }= 1st row and 1st column= 2**

** { a }_{ 32 }****= 3rd row and 2nd column=5 (in the above 3x2 matrix)**

**Column Vector: **

**A column vector has only one column b= {\begin{bmatrix} 2 \\ 5 \\ 1 \end{bmatrix} }_{ 3\times 1 }**

** It has 3 rows and 1 column and it is symbolically denoted as **kx1** vector. This means it has k rows and 1 column.**

**Row Vector:**

**c={ \begin{bmatrix} 2 & 5 & 1 \end{bmatrix} }_{ 1\times 3 } **

**a row vector has 1 row and k columns and it is symbolically denoted as the 1xk vector.**

**Scalar quantity:**

#### A scalar matrix (quantity) is a single number.

** d={ \begin{bmatrix} 5 \end{bmatrix} }_{ 1\times 1 }.**

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