Matrices
Published: 7 Mar 2023
What Are Matrices? A Beginner’s Guide
Get started with matrices with this beginner-friendly guide, covering everything from the start/basics to Matrix Addition, Multiplication, Determinant, Adjoint and Multiplicative Inverse of a Matrix.
This section covers almost all basics like Introduction to Matrices, Types of Matrices, Addition of Matrices and its laws, and Multiplication of Matrices.
Define Matrix:
OR
A matrix is an arrangement of real numbers in rows and columns enclosed in square brackets.
Each number in a matrix is called an element or entry of the matrix. Matrices are mostly denoted by capital letters. Like A, B, C etc.
Examples
$ A=\left[\begin{array}{ll}2 & 3 \\ 0 & 5\end{array}\right] $
$ C=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1\end{array}\right] $
$ D=\left[\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right] $
In this example
2, 5,1,3 all are the elements of a matrix D.
Square Brackets میں Rows اور Columns کے ترتیب کو Matrix کہتے ہیں۔
Matrix میں موجود numbers کو Matrix کے Elements کہتے ہیں۔
Matrixکو عام طور پر Capital Letters سے ظاہر کرتے ہیں۔ جیسے A, B, C
2, 5, 1, 3تمام Matrix کے Elementsہے۔
Rows and Columns of a Matrix
The rows of a matrix run horizontally.
Columns of a Matrix
The columns of a matrix run vertically.
Example
$ A=\left[\begin{array}{ll}2 & 3 \\ 0 & 5\end{array}\right] $
Here 2, 3 and 0, 5 are row of Matrix A. Here 2, 0 and 3, 5 are the columns of Matrix A.
2, 3اور0,5ہمارے ساتھ Matrix کے Rows ہیں۔
0, 2اور3,5ہمارے ساتھ Matrix کے Rows ہیں۔
$ A=\left[\begin{array}{lll} 3 & 5 & 2 \\ 0 & 9 & 8 \end{array}\right] \\ $In this example
3, 5, 2 and 0, 9, 8 are the rows of a matrix A. 3, 0 , 5, 9 and 2, 8 are the columns of matrix A.
3, 5, 2 اور0, 9, 8ہمارے ساتھ Matrix کے Rows ہیں۔
5, 9 , 3, 0 اور 2, 8ہمارے ساتھ Matrix کے Columns ہیں۔
Order or Dimension of a Matrix
Rows اور Columns کی تعداد جو Matrix میں ہوتی ہے اسے Order of a matrix کہا جا تا ہے۔
Order of a matrix is represented by:$ Order \ of \ matrix =m \times n $
OR
$ Order \ of \ matrix = m-by-n $
Here $ “m” $ represents number of Rows
And $ “n” $ represents number of columns
Note:
Order of a matrix is also called dimension or size of a matrix.
Examples
$ D=\left[\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right] $
In this example
As No. of Rows=2 And No. of Columns=2
Rowsکی تعداد “2”ہے۔
Columns تعداد “2”ہے۔
$ So \ order \ is \ 2-by-2 \ (OR) \ 2 \times 2 $Example # 2 $ A=\left[\begin{array}{lll} 3 & 5 & 2 \\ 0 & 9 & 8 \end{array}\right] \\ $
In this example
As No. of Rows $ =2 $
And No. of Columns $ =3 $
Rowsکی تعداد “2”ہے۔
Columns تعداد “3”ہے۔
So order is 2-by-2 (OR) 2×2Equal Matrix
جب دو Matrix کے Order اور تمام Elements ایک جیسے ہو ۔
Example of Equal Matrix
Solution:
$ A=\left[\begin{array}{cc}2 & -3 \\ u & 0\end{array}\right] $
$ B=\left[\begin{array}{cc}v & -3 \\ 5 & w\end{array}\right] $
As A and B are equal. So $ \left[\begin{array}{cc}2 & -3 \\ u & 0\end{array}\right]=\left[\begin{array}{cc}v & -3 \\ 5 & w\end{array}\right] $
Now compare the corresponding elements
$ 2=v $
Or
$ v=2 $
$ u=5 $
$ 0=w $
Or
$ w=0 $
MCQs on Matrix
O Algebra
O Real number
O Matrices
O None
Show Answer
Matrices
2. Each number in a matrix is called ____________ of the matrix.
O Row
O Entry
O Element
O Both b & c
Show Answer
Both b & c
3. Matrices are mostly denoted by ____________ letter.
O Small
O Capital
O Both a & b
O None of these
Show Answer
Capital
4. The ____________ of a matrix run horizontally.
O Row
O Column
O Determinant
O None of these
Show Answer
Row
5. In $ \left[\begin{array}{ll}2 & 5 \\ I & 3\end{array}\right] 2,5, I, 3 $ all are the ____________ of a matrix.
O Row
O Column
O Elements
O None of these
Show Answer
Elements
6. In $ \left[\begin{array}{lll}1 & 2 & 3 \\ a & b & c \\ x & y & z \end{array}\right] 2, b \ and \ y $ are ____________ of a matrix.
O Row
O Column
O Equal
O None of these
Show Answer
Column
7. In $ \left[\begin{array}{lll}1 & 2 & 3 \\ a & b & c \\ x & y & z \end{array}\right] , a, b \ and \ c $ are ____________ of a matrix.
O Row
O Column
O Equal
O None of these
Show Answer
Row
8. In $ \left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], 1,3 \ and \ 2, 4 $ are the ____________ of a matrix.
O Rows
O Columns
O Equal
O None of these
Show Answer
Columns
9. The matrix with $ m $ rows and $ n $ columns has order ____________
O $ m \times n $
O $ m-by-n $
O both a & b
O None of these
Show Answer
both a & b
10. A matrix with represents $ m $ is ____________
O Row
O Column
O Both a & b
O None of these
Show Answer
Row
11. A matrix with represents $ n $ is ____________
O Row
O Column
O Both a & b
O None of these
Show Answer
Column
12. Order of matrix can be written as ____________
O Column by row
O Row by Row
O Row by Column
O All of them
Show Answer
Row by Column
13. The order of matrix $ \left[\begin{array}{lll}1 & 3 & 5 \end{array}\right] $ is ____________.
O $ 2-by-2 $
O $ 3-by-3 $
O $ 1-by-3 $
O $ 3-by-1 $
Show Answer
$ 1-by-3 $
Explanation:
The Matrix consists of One Row and 3 Columns
14. The order of matrix $ \left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] $ is ____________.
O $ 2-by-2 $
O $ 3-by-3 $
O $ 1-by-3 $
O $ 3-by-1 $
Show Answer
$ 2-by-2 $
Explanation:
The matrix consists of 2 Rows and 2 Columns
15. Order of a matrix is also called _______
O Dimension
O Size
O Both a & b
O None of these
Show Answer
Both a & b
Explanation:
Order of a matrix is also called Dimension or Size of a matrix.
16. $ m \times n $ means _______
O $ m \ multiply \ n $
O order of a matrix
O column of a matrix
O Row of a matrix
Show Answer
order of a matrix
Explanation:
$ m \times n $ does not mean the multiplication.
It shows the order of a matrix having rows and columns.
17. Both $ \left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right] $ and $ \left[\begin{array}{ll}1+1 & 3+2 \\ 3+1 & 2+1\end{array}\right] $ are _______
O Equal
O Not equal
O Zero
O None of these
Show Answer
Equal
Explanation:
$ \left[\begin{array}{ll}1+1 & 3+2 \\ 3+1 & 2+1\end{array}\right]=\left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right] $
$ \left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right]=\left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right] $
18. In$ \left[\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right] \ then \ a_{21} $ is _______
O 3
O 2
O 4
O 1
Show Answer
4
Explanation:
$ a_{21} $ means that 2nd Row and First Column. Thus the position of $ a_{21} $ is 4.
19. In $ \left[\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right] \ then \ a_{22} $ is _______
O 3
O 2
O 4
O 1
Show Answer
1
Explanation:
$ a_{22} $ means that 2nd Row and 2nd Column. Thus the position of $ a_{22} $ is 1.
20. In $ \left[\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right] \ then \ a_{12} $ is _______
O 3
O 2
O 4
O 1
Show Answer
2
Explanation:
$ a_{12} $ means that 1st Row and 2nd Column. Thus the position of $ a_{12} $ is 2.
21. In $ \left[\begin{array}{cc}2 & -3 \\ 4 & v\end{array}\right]=\left[\begin{array}{ll}2 & w \\ 6 & 6\end{array}\right] \ then \ w= $ ________
O 2
O 5
O 6
O $ -3 $
Show Answer
$ -3 $
Explanation:
By comparing the corresponding element of $ w \ which \ is \ -3 $
22. If $ \left[\begin{array}{ll}x-1 & 4 \\ y+3 & 7\end{array}\right]=\left[\begin{array}{cc}0 & 4 \\ -2 & -7\end{array}\right] then \ x= \ ? $
O -1
O 0
O 1
O 2
Show Answer
1
Explanation:
By comparing the corresponding element of $ x \ which \ is$
$ x-1=0 $
$ x=1 $
23. If $ \left[\begin{array}{cc}x-1 & 4 \\ y+3 & -7\end{array}\right]=\left[\begin{array}{cc}0 & 4 \\ -2 & -7\end{array}\right] \ then\ y= \ ? $
O $ -5 $
O 5
O 0
O None
Show Answer
$ -5 $
Explanation:
By comparing the corresponding element of $ y \ which \ is$
$ y+3=-2 $
$ y=-2-3 $
$ y=-5 $
Types of Matrices
- Be Respectful
- Stay Relevant
- Stay Positive
- True Feedback
- Encourage Discussion
- Avoid Spamming
- No Fake News
- Don't Copy-Paste
- No Personal Attacks
- Be Respectful
- Stay Relevant
- Stay Positive
- True Feedback
- Encourage Discussion
- Avoid Spamming
- No Fake News
- Don't Copy-Paste
- No Personal Attacks
