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

Tardigrade Admin · Accepted Answer

Let M=[a b c d e f g h i] M [0 1 0]=[-1 2 3] ⇒ b =-1, e =2, h =3 M [1 -1 0]=[1 1 -1] ⇒ a =0, d =3, g =2 M [1 1 1 ]=[0 0 12] ⇒ g + h + i =12 ⇒ i =7 ∴ Sum of diagonal elements =9

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

Let M=⎣⎡​adg​beh​cfi​⎦⎤​ M⎣⎡​010​⎦⎤​=⎣⎡​−123​⎦⎤​ ⇒b=−1,e=2,h=3 M⎣⎡​1−10​⎦⎤​=⎣⎡​11−1​⎦⎤​ ⇒a=0,d=3,g=2 M⎣⎡​111​⎦⎤​=⎣⎡​0012​⎦⎤​ ⇒g+h+i=12⇒i=7 ∴ Sum of diagonal elements =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 the sum of the diagonal entries of $M$ is