Check whether (l + m + n) is a factor of the determinant |(l + m) (m + n) (n + l) n l m 2 2 2| or not. Give Reason

CBSE Class 12 Sample Paper for 2020 Boards
CBSE Class 12 Sample Paper for 2020 Boards
Last updated at Dec. 16, 2024 by Teachoo
Transcript
Question 16 Check whether (l + m + n) is a factor of the determinant |(l + m) (m + n) (n + l) n l m 2 2 2| or not. Give Reason | (l + m n 2 m + n l 2 n + l m 2 )| Applying 𝑅1→ 𝑅 1 + 𝑅2 | (l + m + n n 2 m + n + l l 2 n + l + m m 2 )| Taking (𝑙+𝑚+𝑛) common from 𝑅_1 (l + m + n) | 1 n 2 1 l 2 1 m 2 ] Since (𝑙+𝑚+𝑛) is multiplied outside, it means that is a factor of the determinant