Question
The value of the determinant vmatrix a & b & c \\ l & m & n \\ p & q & r vmatrix is equal to
NDA
Mathematics
Determinants
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. vmatrix a & b & c \\ p & q & r \\ l & m & n vmatrix
- B. vmatrix l & m & n \\ a & b & c \\ p & q & r vmatrix
- C. vmatrix p & q & r \\ a & b & c \\ l & m & n vmatrix
- D. vmatrix a & p & l \\ b & q & m \\ c & r & n vmatrix
Answer
C. vmatrix p & q & r \\ a & b & c \\ l & m & n vmatrix
Step-by-step solution
Let = vmatrix a & b & c \\ l & m & n \\ p & q & r vmatrix Interchanging the first and third rows (R_1 R_3), the sign of the determinant changes: = - vmatrix p & q & r \\ l & m & n \\ a & b & c vmatrix Now, interchanging the second and third rows (R_2 R_3), the sign changes again: = - ( - vmatrix p & q & r \\ a & b & c \\ l & m & n vmatrix ) = vmatrix p & q & r \\ a & b & c \\ l & m & n vmatrix Answer: vmatrix p & q & r \\ a & b & c \\ l & m & n vmatrix
Related: Mathematics — Determinants · All PYQ Banks