If A=[6 8 5 4 2 3 9 7 1] is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is equal to

Question

If A=[6 8 5 4 2 3 9 7 1] is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is equal to (A) [6 6 7 6 2 5 7 5 1] (B) [0 2 -2 -2 5 -2 2 2 0] (C) [6 6 7 -6 2 -5 -7 5 1] (D) [0 6 -2 2 0 -2 -2 -2 0]

Tardigrade Admin · Accepted Answer

We have, A=[6 8 5 4 2 3 9 7 1] ⇒ A prime=[6 4 9 8 2 7 5 3 1] ∵ A=((A+A prime/2))+((A-A prime/2)) Here, (A+A prime/2) is the symmetric part of A and (A-A prime/2) is the skew-symmetric part of A. ∴ We have, symmetric matrix, B=(A+A prime/2) =(1/2) [6 8 5 4 2 3 9 7 1]+[6 4 9 8 2 7 5 3 1] =(1/2)[12 4 10 14 10 2]=[6 2 5 7 5 1]

Q. If $A = ⎣ ⎡ 649827531 ⎦ ⎤$ is the sum of a symmetric matrix $B$ and skew-symmetric matrix $C$ , then $B$ is equal to

$⎣ ⎡ 667625751 ⎦ ⎤$

$⎣ ⎡ 0 - 2 2 252 - 2 - 2 0 ⎦ ⎤$

$⎣ ⎡ 6 - 6 - 7 625 7 - 5 1 ⎦ ⎤$

$⎣ ⎡ 02 - 2 60 - 2 - 2 - 2 0 ⎦ ⎤$

Q. If A=⎣⎡​649​827​531​⎦⎤​ is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is equal to

⎣⎡​667​625​751​⎦⎤​

⎣⎡​0−22​252​−2−20​⎦⎤​

⎣⎡​6−6−7​625​7−51​⎦⎤​

⎣⎡​02−2​60−2​−2−20​⎦⎤​

Q. If $A = ⎣ ⎡ 649827531 ⎦ ⎤$ is the sum of a symmetric matrix $B$ and skew-symmetric matrix $C$ , then $B$ is equal to

$⎣ ⎡ 667625751 ⎦ ⎤$

$⎣ ⎡ 0 - 2 2 252 - 2 - 2 0 ⎦ ⎤$

$⎣ ⎡ 6 - 6 - 7 625 7 - 5 1 ⎦ ⎤$

$⎣ ⎡ 02 - 2 60 - 2 - 2 - 2 0 ⎦ ⎤$