Question

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

14. $\left[\begin{array}{cc}-5& 7\\ 6& 8\end{array}\right]-\left[\begin{array}{ccc}4& 0& -2\\ 9& 0& 1\end{array}\right]$

Short answer

Impossible, since the subtraction of the matrices is $\left[\begin{array}{cc}-5& 7\\ 6& 8\end{array}\right]-\left[\begin{array}{ccc}4& 0& -2\\ 9& 0& 1\end{array}\right]$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 subtraction of the two matrices will also yield a matrix of order $m\times n$wherein each element is the difference of the corresponding elements.

- Represent matrix subtraction in symbols

In order to find $\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]-\left[\begin{array}{ccc}p& q& r\\ s& t& u\\ v& w& x\end{array}\right]$, add 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 subtraction, if possible

Since the dimension of the matrix is and dimension of matrix $\left[\begin{array}{cc}-5& 7\\ 6& 8\end{array}\right]$is $2\times 2$therefore, matrix subtraction $\left[\begin{array}{ccc}4& 0& -2\\ 9& 0& 1\end{array}\right]$is $2\times 3$not possible since the dimension of the matrix is not same.