Q15. - Algebra 2

Question

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

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

Step-by-Step Solution

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 1 - 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.

Step 2 - 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.

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

Step 3 - 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.