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Using the Property of Determinants and Without Expanding, Prove that |(A-b,B-c,C-a),(B-c,C-a,A-b),(A-a,A-b,B-c)| = 0 - Mathematics

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Question

Using the property of determinants and without expanding, prove that:

`|(a-b,b-c,c-a),(b-c,c-a,a-b),(a-a,a-b,b-c)| = 0`

Sum
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Solution

Here, the two rows R1 and R3 are identical.

∴ Δ = 0.

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Chapter 4: Determinants - Exercise 4.2 [Page 119]

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NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 4 Determinants
Exercise 4.2 | Q 2 | Page 119

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