# Example 13 - Chapter 4 Class 12 Determinants

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 13 Evaluate โ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ โ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ We need to obtain 0 in 2nd row as well as 3rd row Applying R2 โ R2 โ R1 โ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ๐ โ๐๏ทฎ๐โ๐๏ทฎ๐๐โ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ๐๏ทฎ๐โ๐๏ทฎ๐(๐โ๐)๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ Applying R3 โ R3 โ R1 = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ0๏ทฎ๐โ๐๏ทฎ๐(๐โ๐)๏ทฎ๐โ๐๏ทฎ๐โ๐๏ทฎ๐๐โ๐๐๏ทฏ๏ทฏ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ0๏ทฎ(๐โ๐)๏ทฎ๐(๐โ๐)๏ทฎ๐๏ทฎ(๐โ๐)๏ทฎ๐(๐โ๐)๏ทฏ๏ทฏ Expanding it along C1 = 1 ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฎ ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏโ0 ๐๏ทฎ๐๐๏ทฎ ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏ +0 ๐๏ทฎ๐๐๏ทฎ ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏ = 1 bโ๐๏ทฏ๏ทฎc ๐โ๐๏ทฏ๏ทฎ cโa๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏ โ 0 + 0 = 1 (b โ a) b(a โ c) โ (c โ a) (c) (a โ b)๏ทฏ = โ(a โ b) b ( โ (c โ a)) โ (c โ a) c (a โ b) = (a โ b) b (c โ a) โ (c โ a) c (a โ b) = (a โ b)(c โ a) (b โ c)) = (a โ b) (b โ c) (c โ a) Thus โ = (a โ b) (b โ c) (c โ a)

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6 Deleted for CBSE Board 2021 Exams only

Example 7 Deleted for CBSE Board 2021 Exams only

Example 8 Deleted for CBSE Board 2021 Exams only

Example 9 Important Deleted for CBSE Board 2021 Exams only

Example 10 Important Deleted for CBSE Board 2021 Exams only

Example 11 Deleted for CBSE Board 2021 Exams only

Example 12 Deleted for CBSE Board 2021 Exams only

Example 13 Deleted for CBSE Board 2021 Exams only You are here

Example 14 Important Deleted for CBSE Board 2021 Exams only

Example 15 Important Deleted for CBSE Board 2021 Exams only

Example 16 Important Deleted for CBSE Board 2021 Exams only

Example 17

Example 18 Important

Example 19

Example 20

Example 21

Example 22

Example 23

Example 24 Important

Example 25

Example 26 Important

Example 27 Deleted for CBSE Board 2021 Exams only

Example 28 Important Deleted for CBSE Board 2021 Exams only

Example 29 Deleted for CBSE Board 2021 Exams only

Example 30

Example 31 Important Deleted for CBSE Board 2021 Exams only

Example 32 Important Deleted for CBSE Board 2021 Exams only

Example 33 Important Deleted for CBSE Board 2021 Exams only

Example 34 Important Deleted for CBSE Board 2021 Exams only

Chapter 4 Class 12 Determinants

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.