Problem

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. $\left[\begin{array}{ll}4 & 10 \\ 1 & 12\end{array}\right]$

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/3PhKBFvfWD/

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