Let A be a 3 × 3 matrix having entries from. the set -1,0,1 . The number of all such matrices A having sum of all the entries equal to 5 , is

Question

Let A be a 3 × 3 matrix having entries from. the set -1,0,1 . The number of all such matrices A having sum of all the entries equal to 5 , is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Case-I: 1 arrow 7 times and -1 arrow 2 times number of possible matrix =(9 !/7 ! 2 !)=36 Case-II: 1 arrow 6 times, -1 arrow 1 times and 0>2 times number of possible matrix =(9 !/6 ! 2 !)=252 Case-III: 1 arrow 5 times, and 0 arrow 4 times number of possible matrix =(9 !/5 ! 4 !)=126 Hence total number of all such matrix A =414

Q. Let A be a 3×3 matrix having entries from. the set {−1,0,1}. The number of all such matrices A having sum of all the entries equal to 5 , is_______

Case-I: 1→7 times and −1→2 times number of possible matrix =7!2!9!​=36 Case-II: 1→6 times, −1→1 times and 0>2 times number of possible matrix =6!2!9!​=252 Case-III: 1→5 times, and 0→4 times number of possible matrix =5!4!9!​=126 Hence total number of all such matrix A =414

Q. Let $A$ be a $3 \times 3$ matrix having entries from. the set ${- 1, 0, 1}$ . The number of all such matrices A having sum of all the entries equal to $5$ , is_______