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# PPT: Determinants GATE Notes | EduRev

## 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/
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