Let M be a 3 × 3 matrix satisfying M[ 0 1 0 ]=[ -1 2 3 ] M[ 1 -1 0 ]=[ 1 1 -1 ], text and M[ 1 1 1 ]=[ 0 0 12 ] then sum of the diagonal entries of M is

Question

Let M be a 3 × 3 matrix satisfying M[ 0 1 0 ]=[ -1 2 3 ] M[ 1 -1 0 ]=[ 1 1 -1 ], text and M[ 1 1 1 ]=[ 0 0 12 ] then sum of the diagonal entries of M is (A) 0 (B) -3 (C) 6 (D) 9

Tardigrade Admin · Accepted Answer

M[1 0 0]=M([1 -1 0]+[0 1 0]) M=[-1 2 3]+[1 1 -1]=[0 3 2] and M[0 0 1]=M([1 1 1]-[1 0 0]-[0 1 0]) =[0 0 12]-[0 3 2]-[-1 2 3]=[1 -5 7] M[1 0 0]=[0 3 0]⇒ m11=0 Similarly, M[0 1 0]=[-1 2 3]⇒ m22=2 and m33=7

Q. Let M be a 3×3 matrix satisfying M⎣⎡​010​⎦⎤​=⎣⎡​−123​⎦⎤​M⎣⎡​1−10​⎦⎤​=⎣⎡​11−1​⎦⎤​, and M⎣⎡​111​⎦⎤​=⎣⎡​0012​⎦⎤​ then sum of the diagonal entries of M is

0

-3

6

9

Q. Let $M$ be a $3 \times 3$ matrix satisfying $M ⎣ ⎡ 010 ⎦ ⎤ = ⎣ ⎡ - 1 23 ⎦ ⎤ M ⎣ ⎡ 1 - 1 0 ⎦ ⎤ = ⎣ ⎡ 11 - 1 ⎦ ⎤, and M ⎣ ⎡ 111 ⎦ ⎤ = ⎣ ⎡ 0012 ⎦ ⎤$
then sum of the diagonal entries of $M$ is