Notes on Matrix | Grade 7 > Optional Maths > Matrix | KULLABS.COM

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Definition

A number arranged in rows and columns which enclosed in large brackets or round brackets with a rectangular arrangement is called matrix. It is represented by capital letters . Here, its plural form is matrices .

For eg ;

A = $$\begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$$ B = $$\begin{bmatrix} 2 & 1 & 3 \\ 6 & 4 & 2 \end{bmatrix}$$

C = $$\begin {bmatrix} 4 & 2 \\ -3 & 2 \\ 1 & 0\end{bmatrix}$$

Rows and colums of a matrix

Matrix is a rectangular arrangement of numbers which contain elements in the form of row and column .Here, a column is usually a vertical line and row is a horizontal line .

eg;

A = $$\begin{bmatrix} 3 & 2 \\ 1 & 5\end{bmatrix}$$

This matrix A has two rows and two columns .

Order of matrix

The number of rows and columns present in a matrix gives the order of a matrix .

eg;

A = $$\begin {bmatrix} 3 & 1 & 2 \\ 5 & 4 & 6 \end {bmatrix}$$

Matrix A has 2 rows and 3 columns So, its order is 2 x 3.And it i read as 2 by 3.

Types of Matrices.

1.Row Matrix

A matrix having only one row is known as a matrix row . It can have any number of columns .

eg; A = $$\begin {bmatrix} -3 & 1 & 2\end{bmatrix}$$

It has only one row .

B = $$\begin{bmatrix} -1 & 2\end {bmatrix}$$

It has only one row .

Column Matrix

2.A matrix having only one column but any number of rows is known as a column matrix .

eg; A =$$\begin{bmatrix} -1 \\2 \\ 3 \end{bmatrix}$$ B = $$\begin {bmatrix} 1 \\ 2 \end{bmatrix}$$

Here, A and B both are matrics have only one column .

3.Rectangular Matrix

A matrix having unequal number of rows and columns is known as a rectangular matrix .But,the number of rows and columns should not be equal .

A = $$\begin{bmatrix} 2 & -3 & 4 \\ 7 & 0 & 1 \end{bmatrix}$$

Here matrix A has 2 rows and 3 columns is unequal .So, it is rectangular matrix .

B = $$\begin{bmatrix} 1 & -4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}$$

4.Zero Matrix

A matrix having each of the elements zero ( 0 ) is known as a null or zero matrix .

O = $$\begin {bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0\end{bmatrix}$$

It is a null matrix which is of order 2 x 3.

Square Matrix

A matrix whose number of rows and columns are equal is called a square matrix .

A = $$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ B = $$\begin{bmatrix} 3 & 2 & 1 \\ 4 & 6 & 5 \\ 7 & 9 & 8 \end{bmatrix}$$

Then, In matrix A and B the number of rows and columns both are equal . So, they are squar matrix.

5.Equal Matrices

A pair of matrices having same order and equal corresponding elements are said to be equal matrices .

eg

A = $$\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$ B = $$\begin{bmatrix} 2 & 3 \\ 4 & 5\end{bmatrix}$$

Here, matrices A and B are said to be equal matrices as their order is same as well as their corresponding elements are equal .

6.Operation on matrices

In this level we shall only see how matrices are added and subtracted . Let's look at the following examples.

A = $$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ and B = $$\begin{bmatrix} 5 & 6 \\ 7 & 8\end{bmatrix}$$

A + B = ?

Here, as the order of both the matrices is 2 x 2. we can add them

then, A + B = $$\begin {bmatrix} 1 + 5 & 2 + 6 \\ 3 + 7 & 4 +8 \end{bmatrix}$$ [ We add the corresponding elements ]

=$$\begin{bmatrix} 6 & 8\\ 10 & 12 \end{bmatrix}$$

Again,

A = $$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ C = $$\begin{bmatrix} 5 \\ 6 \end{bmatrix}$$

A + C = ? [ Order is not equal so, no addition is possible ]

= $$\begin{bmatrix} 1 & 2 \\ 3 & 4\end{bmatrix}$$ + $$\begin{bmatrix} 5 \\ 6 \end{bmatrix}$$

As the order of these two matrices A and C are not the same we can not add them .

Now,

B - A = ?

so, B - A

= $$\begin{bmatrix} 5 - 1 & 6 - 2 \\ 7 - 3 & 8 - 4 \end{bmatrix}$$

= $$\begin{bmatrix} 4 & 4 \\ 4 & 4\end{bmatrix}$$

• The column is usually a vertical line and row is a horizontal line .
• Matrix is represented by capital letters .
• Its plural form is matrices .
.

#### Click on the questions below to reveal the answers

Solution

A order 2$$\times$$3

It means matrix   A should have  2 rows and 3 columns.

A = $$\begin {bmatrix} 1&2&5\\ 2&4&6\\\end {bmatrix}$$

Solution

Here, C order 3$$\times$$3

It means  matrix C must have 3 rows and 3 columns.

C=  $$\begin {bmatrix} 2 & 5& 8\\ 1 & 4 & 7 \\ 3 & 6 & 9\\\end {bmatrix}$$

Solution

A= $$\begin {bmatrix}2&5 \\ -5&3 \\ 9&7 \\\ \end {bmatrix}$$

This is rectangular matrix.

It's order is 3 $$\times$$ 2.

Solution

P= $$\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}$$

Here, Rows present in matrix P= 3

Columns present in matrix  p = 3

Therefore, Order of Matrix = 3 $$\times$$ 3

Solution

$$\begin {bmatrix} a&5\\6&b\end {bmatrix}$$ =  $$\begin {bmatrix} 7&c\\d&4\end {bmatrix}$$

Here, As the matrices are equal, their corresponding elements are also equal.

So, a = 7, b = 4, c = 5 and d = 6.

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• ### A matrix having  any number of columns but having only one row is called a ............................

row matrix.
Rectangular matrix
Zero or null matrix
Column matrix
• ### A matrix  whose number of rows and columns are equal is known as a ..................................

Rectangular matrix
Row matrix
Square matrix
Column matrix
• ### Which type of  matrix is this?  A= (egin{bmatrix}1&2end {bmatrix})

It is a square matrix.
It is a column matrix.
It is a null matrix.
It is a row matrix.
• ### A matrix as it is a ................................... of numbers will contain elements in the form of row and column.

Column of matrix
zero matrix
recetangular arrangement
order of matrix

Two
One
Zero
Equal
• ### Matrix is represented by capital letters. Its plural form is ..................

Horizontal
matrices
Columns of matrix
Order of matrices
• ### The horizontal line is called.................... and verticle line is called..............................

equal, square
matrix, columns
Zero, null matrix
rows, columns
• ### A matrix whose number of rows and columns are equal is known as a .....................................

Square matrix
Row matrix
Null matrix
order of matrix
• ### The number of rows and columns present in a matrix gives the ...............................

Order of the matrix
Rows and columns of the matrix
Zero or null matrix
Rectangular matrix

elements
numbers
Columns
rows

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