Respuesta :
Answer:
[tex]b_{11}=-14,b_{12}=9,b_{13}=8,b_{21}=4,b_{22}=-1,b_{23}=0[/tex]
Step-by-step explanation:
The given matrix addition is
[tex]B+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}[/tex]
We need to find the elements of matrix B.
Let [tex]B=\begin{bmatrix}b_{11}&b_{12}&b_{13}\\ b_{21}&b_{22}&b_{23}\end{bmatrix}[/tex]
Substitute the value of matrix.
[tex]\begin{bmatrix}b_{11}&b_{12}&b_{13}\\ b_{21}&b_{22}&b_{23}\end{bmatrix}+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}[/tex]
After addition of two matrix we get
[tex]\begin{bmatrix}b_{11}+15&b_{12}-7&b_{13}+4\\ b_{21}+0&b_{22}+1&b_{23}+2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}[/tex]
On equating both sides.
[tex]b_{11}+15=1\Rightarrow b_{11}=-14[/tex]
[tex]b_{12}-7=2\Rightarrow b_{12}=9[/tex]
[tex]b_{13}+4=12\Rightarrow b_{13}=8[/tex]
[tex]b_{21}+0=4\Rightarrow b_{21}=4[/tex]
[tex]b_{22}+1=0\Rightarrow b_{22}=-1[/tex]
[tex]b_{23}+2=2\Rightarrow b_{23}=0[/tex]
Therefore, the elements of matrix B are [tex]b_{11}=-14,b_{12}=9,b_{13}=8,b_{21}=4,b_{22}=-1,b_{23}=0[/tex].
