Question
Let S= \ A= ( array lll 0 & 1 & c \\ 1 & a & d \\ 1 & b & e array ): a, b, c, d, e \ 0,1\ . and .|A| \ -1,1\ \ , where |A| denotes the determinant of A. Then the number of elements in S is
JEE Advanced
Mathematics
Determinants
2024
JEE Advanced 2024 (Paper 1)
JEE Advanced Mathematics Question (2024) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
\(|A|=-(e-d)+c(b-a)= 1\) Case (i) : \(c=0 (e, d)=(1,0),(0,1) 2\) ways b and a can be each 2 ways \( \) Total \(=8\) ways Case (ii) : \(c 0 c=1\) \( d-e+b-a= 1\) \( . array llll 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 array \ 4 2=8\) ways Total \(=16\) ways
Related: Mathematics — Determinants · All PYQ Banks