Question

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

4.$\left[\begin{array}{ccc}5& 8& -4\end{array}\right]+\left[\begin{array}{cc}12& 5\end{array}\right]$

Short answer

Impossible, since the subtraction of the matrices is$\left[\begin{array}{ccc}5& 8& -4\end{array}\right]+\left[\begin{array}{cc}12& 5\end{array}\right]$ doesn’t exist.

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 addition of the corresponding elements.

- Represent matrix addition in symbols

In order to find$\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]+\left[\begin{array}{ccc}p& q& r\\ s& t& u\\ v& w& x\end{array}\right]$, subtract corresponding elements of both the matrices.

$\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]+\left[\begin{array}{ccc}p& q& r\\ s& t& u\\ v& w& x\end{array}\right]=\left[\begin{array}{ccc}a+p& b+q& c+r\\ d+s& e+t& f+u\\ g+v& h+w& i+x\end{array}\right]$

- Perform the matrix addition, if possible

Since the dimension of the matrix $\left[\begin{array}{ccc}5& 8& -4\end{array}\right]$is $1\times 3$ and dimension of matrix $\left[\begin{array}{cc}12& 5\end{array}\right]$is $1\times 2$, therefore, matrix addition is not possible since the dimension of the matrix is not same..