The document discusses determinants, which are mathematical constructs denoted by a specific symbol and can be of different orders (1st, 2nd, 3rd). It provides examples of calculating determinants and outlines several properties, such as invariance under transposition and conditions that lead to a determinant value of zero. The document concludes by inviting questions and suggestions from the audience.

1. DETERMINANT
PRESENTED BY:-
GROUP-A
ROHAN SINGHA,RAHUL DEY, CHANDARNI SHATRADHAR ,PANKAJ SAHU, TANMOY PANDA,
YOGESH KUMAR
BBA(H) 2ND SEMESATAR 1ST YEAR
EMINENT COLLEGE OF MANAGEMENT AND TECHNOLOGY

2. INTRODUCE DETERMINANT:-
 The Determinant is denoted by this symbol
 Determinant define as order of 2,3 and 1 successively.
 As a example of First order determinant 15 = 15
 Second order of Determinant
3 4
5 6
=(3× 6) − 4 × 5
=18-20
=-2
 Third order of Determinant
2 3 2
2 3 2
3 4 2
=2
3 2
4 2
-3
2 2
3 2
+2
2 3
3 4
= 2(6−8) − 3 4 − 6 + 2 8 − 9
=-4+6-2
=0

3. PROPERTIES OF DETERMINANT
 Property:-1
The value of a determinant is unaltered if the determinant is
transposed, i.e. if rows and columns are interchanged.
625 564 −64
−560 360 257
951 −960 842
=
625 −560 951
564 360 −960
−64 257 842

4.  Property:-2
The value of a determinant is unaltered but the sign is
altered if two adjacent rows and columns are
interchanged.
5 2 1
41 578 2325
4114 5254 4574
= -
2 5 1
578 41 2325
5254 4114 4574

5.  Property:-3
If all the elements of one row or one column are
multiplied by a number then the value of the
determinant is multiplied by that number.
2596 3244 5230
525 658 53
25 4154 4578
= 2
1298 1622 2615
525 658 53
25 4154 4578

6.  Property:-5
If each element of a row or column is expressed as the sum
of two numbers then the determinant can be expressed as
sum of two determinants.
𝑎 + 𝑥 𝑏 𝑐
𝑑 + 𝑦 𝑒 𝑓
𝑔 + 𝑧 ℎ 𝑖
=
𝑎 𝑏 𝑐
𝑑 𝑒 𝑓
𝑔 ℎ 𝑖
+
𝑥 𝑏 𝑐
𝑦 𝑒 𝑓
𝑧 𝑔 ℎ

7.  Property:-6
If two rows or columns of a determinant are
identical then the value of the determinant is 0.
4556 2685 4556
1285 3565 1285
598 2356 598
=0

8. THANK
YOU
ANY QUESTION
AND
SUGGESTION