Question

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

14.$\left[\begin{array}{c}4\\ 1\\ -2\end{array}\right]+\left[\begin{array}{c}6\\ -5\\ 8\end{array}\right]$

Short answer

The addition of the matrices is$\left[\begin{array}{c}4\\ 1\\ -2\end{array}\right]+\left[\begin{array}{c}6\\ -5\\ 8\end{array}\right]=\left[\begin{array}{c}10\\ -4\\ 7\end{array}\right]$.

Step-by-step solution

- Define concept of matrix addition

If A and B are two matrices of order $m\times n$, then the addition of the two matrices will also yield a matrix of order $m\times n$wherein each element is the sum of the corresponding elements.

- Add corresponding elements

In order to find $\left[\begin{array}{c}4\\ 1\\ -2\end{array}\right]+\left[\begin{array}{c}6\\ -5\\ 8\end{array}\right]$, add corresponding elements of both the matrices.

$\left[\begin{array}{c}4\\ 1\\ -2\end{array}\right]+\left[\begin{array}{c}6\\ -5\\ 8\end{array}\right]=\left[\begin{array}{c}4+6\\ 1-5\\ -1+8\end{array}\right]$

- Simplify the matrix

Further simplify the matrix by adding the elements.

$\begin{array}{c}\left[\begin{array}{c}4\\ 1\\ -2\end{array}\right]+\left[\begin{array}{c}6\\ -5\\ 8\end{array}\right]=\left[\begin{array}{c}4+6\\ 1-5\\ -1+8\end{array}\right]\\ =\left[\begin{array}{c}10\\ -4\\ 7\end{array}\right]\end{array}$