Ex 4.2, 4

Last updated at Dec. 8, 2016 by Teachoo

Ex 4.2, 4 - Using property of determinants |1 bc a(b + c)| - Two rows or columns same

Transcript

Ex 4.2, 4 Using the property of determinants and without expanding, prove that: 1﷮𝑏𝑐﷮𝑎(𝑏+𝑐)﷮1﷮𝑐𝑎﷮𝑏(𝑐+𝑎)﷮1﷮𝑎𝑏﷮𝑐(𝑎+𝑏)﷯﷯ = 0 1﷮𝑏𝑐﷮𝑎(𝑏+𝑐)﷮1﷮𝑐𝑎﷮𝑏(𝑐+𝑎)﷮1﷮𝑎𝑏﷮𝑐(𝑎+𝑏)﷯﷯ = 1﷮𝑏𝑐﷮𝑎𝑏+𝑎𝑐﷮1﷮𝑐𝑎﷮𝑏𝑐+𝑏𝑎﷮1﷮𝑎𝑏﷮𝑐𝑎+𝑐𝑏﷯﷯ C3 → C3 + C2 = 1﷮𝑏𝑐﷮𝑎𝑏+𝑎𝑐+𝑏𝑐﷮1﷮𝑐𝑎﷮𝑏𝑐+𝑏𝑎+𝑏𝑐﷮1﷮𝑎𝑏﷮𝑐𝑎+𝑐𝑏+𝑏𝑐﷯﷯ = 1﷮𝑏𝑐﷮𝑎𝑏+𝑎𝑐+𝑏𝑐﷮1﷮𝑐𝑎﷮𝑏𝑐+𝑏𝑎+𝑏𝑐﷮1﷮𝑎𝑏﷮𝑐𝑎+𝑐𝑏+𝑏𝑐﷯﷯ = (𝑎𝑏+𝑎𝑐+𝑏𝑐) 1﷮𝑏𝑐﷮1﷮1﷮𝑐𝑎﷮1﷮1﷮𝑎𝑏﷮1﷯﷯ C1 and C3 is same = 0

Ex 4.2

Ex 4.2, 4 You are here

Ex 4.3 →

Chapter 4 Class 12 Determinants

Serial order wise

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