Respuesta :
Answer:
The correct option is c.
Step-by-step explanation:
Given information: A, B, and C represent three matrices of the same size and (A + B) + C = 0.
Let the size of A, B, and C is m×n.
[tex]A=\begin{bmatrix}a_{11}} & a_{12}} &...& a_{1n}\\ a_{21}} & a_{22}} &...& a_{2n}\\ ... & ... & ... & ...\\ a_{m1}} & a_{m2}} &...& a_{mn}\\ \end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}b_{11}} & b_{12}} &...& b_{1n}\\ b_{21}} & b_{22}} &...& b_{2n}\\ ... & ... & ... & ...\\ b_{m1}} & b_{m2}} &...& b_{mn}\\ \end{bmatrix}[/tex]
[tex]C=\begin{bmatrix}c_{11}} & c_{12}} &...& c_{1n}\\ c_{21}} & c_{22}} &...& c_{2n}\\ ... & ... & ... & ...\\ c_{m1}} & c_{m2}} &...& c_{mn}\\ \end{bmatrix}[/tex]
It is given that
(A + B) + C = 0
[tex]\begin{bmatrix}a_{11}} & a_{12}} &...& a_{1n}\\ a_{21}} & a_{22}} &...& a_{2n}\\ ... & ... & ... & ...\\ a_{m1}} & a_{m2}} &...& a_{mn}\\ \end{bmatrix}+\begin{bmatrix}b_{11}} & b_{12}} &...& b_{1n}\\ b_{21}} & b_{22}} &...& b_{2n}\\ ... & ... & ... & ...\\ b_{m1}} & b_{m2}} &...& b_{mn}\\ \end{bmatrix}+\begin{bmatrix}c_{11}} & c_{12}} &...& c_{1n}\\ c_{21}} & c_{22}} &...& c_{2n}\\ ... & ... & ... & ...\\ c_{m1}} & c_{m2}} &...& c_{mn}\\ \end{bmatrix}=0[/tex]
[tex]\begin{bmatrix}a_{11}+b_{11}+c_{11} & a_{12}+b_{12}+c_{12} &...& a_{1n}+b_{1n}+c_{1n}\\ a_{21}+b_{21}+c_{21} & a_{22}+b_{22}+c_{22} &...& a_{2n}+b_{2n}+c_{2n}\\ ... & ... & ... & ...\\ a_{m1}+b_{m1}+c_{m1} & a_{m2}+b_{m2}+c_{m2} &...& a_{mn}+b_{mn}+c_{mn}\\ \end{bmatrix}=\begin{bmatrix}0 & 0 & ... & 0\\ 0 & 0 & ... & 0\\ ... & ... & ... & ...\\ 0 & 0 & ... &0 \end{bmatrix}[/tex]
By comparing first element of first row on both the sides, we get
[tex]a_{11}+b_{11}+c_{11}=0[/tex]
[tex]a_{11}+(b_{11}+c_{11})=0[/tex]
Therefore the correct option is c.
