Add the following matrices and enter the final answer in the boxes below, one element per box. $$ \left[\begin{array}{cccc}7 & -3 & 5 & 1 \ 2 & -6 & 7 & 3 \ 4 & 10 & -7 & 0\end{array} ight]+2\left[\begin{array}{cccc}1 & 0 & 2 & 3 \ -1 & 4 & 5 & -7 \ 6 & 1 & 1 & -8\end{array} ight]= $$ ?

Question

Add the following matrices and enter the final answer in the boxes below, one element per box. $$ \left[\begin{array}{cccc}7 & -3 & 5 & 1 \ 2 & -6 & 7 & 3 \ 4 & 10 & -7 & 0\end{array}ight]+2\left[\begin{array}{cccc}1 & 0 & 2 & 3 \ -1 & 4 & 5 & -7 \ 6 & 1 & 1 & -8\end{array}ight]= $$ ?

UpStudy AI · Accepted Answer

To add the given matrices, follow these steps:

1. **Multiply the second matrix by 2:**

$$
2 \times \begin{bmatrix}
1 & 0 & 2 & 3 \
-1 & 4 & 5 & -7 \
6 & 1 & 1 & -8
\end{bmatrix} =
\begin{bmatrix}
2 & 0 & 4 & 6 \
-2 & 8 & 10 & -14 \
12 & 2 & 2 & -16
\end{bmatrix}
$$

2. **Add the resulting matrix to the first matrix:**

$$
\begin{bmatrix}
7 & -3 & 5 & 1 \
2 & -6 & 7 & 3 \
4 & 10 & -7 & 0
\end{bmatrix} +
\begin{bmatrix}
2 & 0 & 4 & 6 \
-2 & 8 & 10 & -14 \
12 & 2 & 2 & -16
\end{bmatrix} =
\begin{bmatrix}
9 & -3 & 9 & 7 \
0 & 2 & 17 & -11 \
16 & 12 & -5 & -16
\end{bmatrix}
$$

**Final Answer:**

$$
\begin{bmatrix}
\boxed{9} & \boxed{-3} & \boxed{9} & \boxed{7} \
\boxed{0} & \boxed{2} & \boxed{17} & \boxed{-11} \
\boxed{16} & \boxed{12} & \boxed{-5} & \boxed{-16}
\end{bmatrix}
$$
$$ \begin{bmatrix} 9 & -3 & 9 & 7 \ 0 & 2 & 17 & -11 \ 16 & 12 & -5 & -16 \end{bmatrix} $$

Add the following matrices and enter the final answer in the boxes below, one element per box. \( \left[\begin{array}{cccc}7 & -3 & 5 & 1 \\ 2 & -6 & 7 & 3 \\ 4 & 10 & -7 & 0\end{array}\right]+2\left[\begin{array}{cccc}1 & 0 & 2 & 3 \\ -1 & 4 & 5 & -7 \\ 6 & 1 & 1 & -8\end{array}\right]= \) ?

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