Answer:
[tex]a_{11}=-11[/tex]
[tex]a_{12}=-16[/tex]
[tex]a_{13}=6[/tex]
[tex]a_{14}=-10[/tex]
Step-by-step explanation:
Let,
[tex]A=\begin{bmatrix}a_{11} & a_{12} & a_{13} & a_{14}\end{bmatrix}[/tex]
We have,
[tex]A+\begin{bmatrix}11 & 17 & -8 & 13\end{bmatrix}=\begin{bmatrix}0& 1& -2& 3\end{bmatrix}[/tex]
[tex]\implies \begin{bmatrix}a_{11} & a_{12} & a_{13} & a_{14}\end{bmatrix}+\begin{bmatrix}11 & 17 & -8 & 13\end{bmatrix}= \begin{bmatrix}0 & 1 & -2& 3\end{bmatrix}[/tex]
By matrix addition,
[tex]\begin{bmatrix}a_{11}+11 & a_{12}+ 17 & a_{13}-8 & a_{14}+13 \end{bmatrix}= \begin{bmatrix}0& 1 & -2& 3\end{bmatrix}[/tex]
By comparing,
[tex]a_{11} + 11 = 0\implies a_{11}=0-11=-11[/tex]
[tex]a_{12}+17 = 1\implies a_{12} =1-17= -16[/tex]
[tex]a_{13}-8 = -2\implies a_{13} =-2 + 8 =6[/tex]
[tex]a_{14}+13 = 3\implies a_{14} = 3 - 13 = -10[/tex]
