PPT: Determinants GATE Notes | EduRev

Engineering Mathematics

GATE : PPT: Determinants GATE Notes | EduRev

 Page 1


DETERMINANTS
• A Determinant of a matrix represents a single 
number. 
• We obtain this value by multiplying and 
adding its elements in a special way. 
Page 2


DETERMINANTS
• A Determinant of a matrix represents a single 
number. 
• We obtain this value by multiplying and 
adding its elements in a special way. 
Determinant of a Matrix of Order One
• Determinant of a matrix of order one 
A=[a
11
]
1x1
is  
?? = a
11
= a
11
Page 3


DETERMINANTS
• A Determinant of a matrix represents a single 
number. 
• We obtain this value by multiplying and 
adding its elements in a special way. 
Determinant of a Matrix of Order One
• Determinant of a matrix of order one 
A=[a
11
]
1x1
is  
?? = a
11
= a
11
Determinant of a Matrix of Order Two
• Determinant of a Matrix A=
?? 11
?? 12
?? 21
?? 22
2x2
is
?? = 
?? 11
?? 12
?? 21
?? 22
= ?? 11
?? 22
-?? 12
?? 21
Page 4


DETERMINANTS
• A Determinant of a matrix represents a single 
number. 
• We obtain this value by multiplying and 
adding its elements in a special way. 
Determinant of a Matrix of Order One
• Determinant of a matrix of order one 
A=[a
11
]
1x1
is  
?? = a
11
= a
11
Determinant of a Matrix of Order Two
• Determinant of a Matrix A=
?? 11
?? 12
?? 21
?? 22
2x2
is
?? = 
?? 11
?? 12
?? 21
?? 22
= ?? 11
?? 22
-?? 12
?? 21
Determinant of a Matrix of Order Three
• Determinant of a Matrix  A = 
?? 11
?? 12
?? 13
?? 21
?? 22
?? 23
?? 31
?? 32
?? 33
is  (expanding along R
1
)
• ?? = 
?? 11
?? 12
?? 13
?? 21
?? 22
?? 23
?? 31
?? 32
?? 33
= (-1)
1+1
?? 11
?? 22
?? 23
?? 32
?? 33
- (-1)
1+2
?? 12
?? 21
?? 23
?? 31
?? 33
+ (-1)
1+3
?? 13
?? 21
?? 22
?? 31
?? 32
= ?? 11
(?? 22
?? 33
-?? 32
?? 23
) -?? 12
(?? 21
?? 33
-?? 31
?? 23
) +  ?? 13
(?? 21
?? 32
-?? 31
?? 22
) 
= ?? 11
?? 22
?? 33
-?? 11
?? 32
?? 23
-?? 12
?? 21
?? 33
+ ?? 12
?? 31
?? 23
+ ?? 13
?? 21
?? 32
-?? 13
?? 31
?? 22
Page 5


DETERMINANTS
• A Determinant of a matrix represents a single 
number. 
• We obtain this value by multiplying and 
adding its elements in a special way. 
Determinant of a Matrix of Order One
• Determinant of a matrix of order one 
A=[a
11
]
1x1
is  
?? = a
11
= a
11
Determinant of a Matrix of Order Two
• Determinant of a Matrix A=
?? 11
?? 12
?? 21
?? 22
2x2
is
?? = 
?? 11
?? 12
?? 21
?? 22
= ?? 11
?? 22
-?? 12
?? 21
Determinant of a Matrix of Order Three
• Determinant of a Matrix  A = 
?? 11
?? 12
?? 13
?? 21
?? 22
?? 23
?? 31
?? 32
?? 33
is  (expanding along R
1
)
• ?? = 
?? 11
?? 12
?? 13
?? 21
?? 22
?? 23
?? 31
?? 32
?? 33
= (-1)
1+1
?? 11
?? 22
?? 23
?? 32
?? 33
- (-1)
1+2
?? 12
?? 21
?? 23
?? 31
?? 33
+ (-1)
1+3
?? 13
?? 21
?? 22
?? 31
?? 32
= ?? 11
(?? 22
?? 33
-?? 32
?? 23
) -?? 12
(?? 21
?? 33
-?? 31
?? 23
) +  ?? 13
(?? 21
?? 32
-?? 31
?? 22
) 
= ?? 11
?? 22
?? 33
-?? 11
?? 32
?? 23
-?? 12
?? 21
?? 33
+ ?? 12
?? 31
?? 23
+ ?? 13
?? 21
?? 32
-?? 13
?? 31
?? 22
• http://www.authorstream.com/Presentation/j
oshsmith1110-162211-determinants-math-
ppt-shella-paglinawan-education-powerpoint/
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Summary

,

pdf

,

PPT: Determinants GATE Notes | EduRev

,

shortcuts and tricks

,

mock tests for examination

,

Sample Paper

,

PPT: Determinants GATE Notes | EduRev

,

Semester Notes

,

Extra Questions

,

past year papers

,

Previous Year Questions with Solutions

,

video lectures

,

practice quizzes

,

PPT: Determinants GATE Notes | EduRev

,

Free

,

MCQs

,

study material

,

Viva Questions

,

Important questions

,

Objective type Questions

,

ppt

,

Exam

;