January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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Example
Write the cofactors of elements of second row of the determinant
D 5
123
2436
2 279
and hence find the value of the determinant.
Solution
Here
A
21
5 ð21Þ
211
23
279
52ð18 1 21Þ5239
A
22
5 ð21Þ
212
13
29
5 9 2 6 5 3
A
23
5 ð21Þ
213
12
2 27
52ð27 2 4Þ5 11
So
A
21
5239; A
22
5 3; and A
23
5 11
Now
D 5 a
21
A
21
1 a
22
A
22
1 a
23
A
23
5 ð24Þð239Þ1 3ð3Þ1 6ð11Þ5 231
3.8 Properties of Determinants
Following properties may be helpful to find the values of determinants:
P1: If any two rows or columns of a determinant are identical, then its value equals
zero.
Example
231
2342
231
5 0 ½The first and second rows are identical:
P2: If all the elements in ...
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