Example 6
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Example 6 Verify Property 1 for Δ = 2−3560415−7 Expanding the determinant along first row, ∆ = 2 045−7 - (-3) 641−7 + 5 6015 = 2(0(– 7) – 5(4) + 3 (6( – 7) – (1) (4)) +5 (6(5) – 1 (0)) = 2(0 – 20) + 3 (-42 – 4) + 5 (30 – 0) = 2 (– 20) +3 (– 46) + 5 (30) = – 40 – 138 + 150 = – 28 By interchanging rows and columns , we get ∆1 = 261−30554−7 ∆1 = 2 054−7 – 6 −355−7 + 1 −3054 = 2(0(– 7) – 4(5) – 6( – 3 (– 7) – 5 (5)) +1 (– 3 (4) – 5 (0)) = 2 (0 – 20) – 6 (+ 21 – 25 ) +1 (– 12 + 0) = 2 ( – 20) – 6 ( – 4) + 1 ( – 12) = – 40 + 24 – 12 = – 52 + 24 = – 28 Hence ∆1 = ∆ Hence ∆1 = ∆ ∴ Property 1 is verified. i.e. If we interchange row & Columns, value of determinant remains unchanged
Examples
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Example 6 You are here
Example 7
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Example 11
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Example 14 Important
Example 15 Important
Example 16 Important
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
Example 28
Example 29
Example 30
Example 31
Example 32 Important
Example 33
Example 34 Important
Chapter 4 Class 12 Determinants
Serial order wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.