Let $A=\left[\begin{array}{ll}2 & 3 \\ 2 & 6\end{array}\right]$ and $B=\left[\begin{array}{rr}0 & 4 \\ -1 & 6\end{array}\right]$. Find $2 A+B$.
A. $\left[\begin{array}{ll}4 & 14 \\ 2 & 24\end{array}\right]$
B. $\left[\begin{array}{rr}4 & 7 \\ 3 & 12\end{array}\right]$
c. $\left[\begin{array}{ll}4 & 10 \\ 3 & 18\end{array}\right]$
D. $\left[\begin{array}{ll}4 & 10 \\ 1 & 12\end{array}\right]$
Answer
\(\boxed{\left[\begin{array}{ll}4 & 10 \\ 3 & 18\end{array}\right]}\) is the final answer.
Step 1 ：Find \(2A\) by multiplying each element in matrix \(A\) by 2: \(2A = 2*\left[\begin{array}{ll}2 & 3 \\ 2 & 6\end{array}\right] = \left[\begin{array}{ll}4 & 6 \\ 4 & 12\end{array}\right]\)
Step 2 ：Add \(2A\) to \(B\) by adding the corresponding elements in each matrix: \(2A + B = \left[\begin{array}{ll}4 & 6 \\ 4 & 12\end{array}\right] + \left[\begin{array}{rr}0 & 4 \\ -1 & 6\end{array}\right] = \left[\begin{array}{ll}4 & 10 \\ 3 & 18\end{array}\right]\)
Step 3 ：\(\boxed{\left[\begin{array}{ll}4 & 10 \\ 3 & 18\end{array}\right]}\) is the final answer.
