Question
If X= [ array l x \\ y \\ z array ] is a solution of the system of equations A X=B, where adj A= [ array ccc 4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3 array ] and B = [ array l 4 \\ 0 \\ 2 array ], then |x+y+z| is equal to :
JEE Main
Mathematics
Matrices
2026
JEE Main 2026 (22 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2
- B. 3 2
- C. 1
- D. 3
Answer
A. 2
Step-by-step solution
X = 1 |A| adj (A) B. | adj (A)| = 4(10)-2(-20)+2(10) = 100, so |A|^2=100 |A|= 10. adj (A) B = pmatrix 16+0+4\\-20+0+10\\4+0+6 pmatrix = pmatrix 20\\-10\\10 pmatrix x+y+z = 20-10+10 |A| = 20 10 = 2 |x+y+z|=2
Related: Mathematics — Matrices · All PYQ Banks