Question 3 - Properties of Determinant - Chapter 4 Class 12 Determinants
Last updated at April 16, 2024 by Teachoo
Properties of Determinant
Question 2 Important
Question 3 You are here
Question 4
Question 5 Important
Question 6 Important
Question 7 Important
Question 8 (i) Important
Question 8 (ii)
Question 9 Important
Question 10 (i)
Question 10 (ii) Important
Question 11 (i)
Question 11 (ii) Important
Question 12 Important
Question 13 Important
Question 14 Important
Question 15 (MCQ) Important
Question 16 (MCQ)
Properties of Determinant
Last updated at April 16, 2024 by Teachoo
Question 3 Using the property of determinants and without expanding, prove that: |■8(2&7&65@3&8&75@5&9&86)| = 0 |■8(2&7&65@3&8&75@5&9&86)| Applying C3 → C3 − C1 = |■8(2&7&𝟔𝟓−𝟐@3&8&𝟕𝟓−𝟑@5&9&𝟖𝟔−𝟓)| = |■8(2&7&63@3&8&72@5&9&81)| Rough 65 – 2 = 63, 63/7 = 9 75 – 3 = 72, 72/8 = 9 86 – 5 = 81, 81/9 = 9 = |■8(2&7&𝟗 × 7@3&8&𝟗 ×8@5&9&𝟗 × 9)| Taking out 9 common from C3 = 9 |■8(2&𝟕&𝟕@3&𝟖&𝟖@5&𝟗&𝟗)| Here, C2 and C3 are identical = 9 × 0 = 0 Thus, |■8(2&7&65@3&8&75@5&9&86)| = 0 Hence proved Using Property: If any two row or column are identical, then value of determinant is zero