Answer:
C.[tex]C=\begin{bmatrix}4&2& -7\end{bmatrix}[/tex]
Step-by-step explanation:
We are given that an equation
[tex]\begin{bmatrix}-18&3&5\end{bmatrix}-C=\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]
We have to find the value of C.
Let C=[tex]\begin{bmatrix}a&b& c\end{bmatrix}[/tex]
[tex]\begin{bmatrix}-18&3&5\end{bmatrix}-\begin{bmatrix}a&b& c\end{bmatrix}=\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]
[tex]\begin{bmatrix}-18-a&3-b& 5-c\end{bmatrix}=\begin{bmatrix}-22&1& 12\end{bmatrix}[/tex]
When two matrix are equal then each element equals to its corresponding element.
Therefore, -18-a=-22
[tex]a=-18+22=4[/tex]
[tex]3-b=1[/tex]
[tex]b=3-1=2[/tex]
[tex]5-c=12[/tex]
[tex]c=5-12=-7[/tex]
Substitute the values then we get
[tex]C=\begin{bmatrix}4&2& -7\end{bmatrix}[/tex]
Hence, option C is true.
