Chapter 3.5, Problem 4CYU

To determine

To calculate: The value of the matrix $\left[\begin{array}{ll}7\hfill & -12\hfill \\ 15\hfill & 4\hfill \end{array}\right]-\left[\begin{array}{ll}9\hfill & 6\hfill \\ 4\hfill & -9\hfill \end{array}\right]$ .

Answer to Problem 4CYU

The value of the matrixis $\left[\begin{array}{ll}-2\hfill & -18\hfill \\ 11\hfill & 13\hfill \end{array}\right]$ .

Explanation of Solution

Given information:

The matrix expression $\left[\begin{array}{ll}7\hfill & -12\hfill \\ 15\hfill & 4\hfill \end{array}\right]-\left[\begin{array}{ll}9\hfill & 6\hfill \\ 4\hfill & -9\hfill \end{array}\right]$ .

Formula used:

The operation on matrices is possible only if the two or more matrices have same order. If $\text{A}=\left[a_{ij}\right]$ and $\text{B}=\left[b_{ij}\right]$ are two matrices of same order, say $m\times n$ , then sum or difference of two matrices is defined as matrix $\text{C}={\left[c_{ij}\right]}_{m\times n}$ , where $c_{ij}=a_{ij}+b_{ij}$ , for all possible values of $i\text{ and }j$ .

Calculation:

Consider the provided expression $\left[\begin{array}{ll}7\hfill & -12\hfill \\ 15\hfill & 4\hfill \end{array}\right]-\left[\begin{array}{ll}9\hfill & 6\hfill \\ 4\hfill & -9\hfill \end{array}\right]$ .

Recall that operation on matrices is possible only if the two or more matrices have same order. If $\text{A}=\left[a_{ij}\right]$ and $\text{B}=\left[b_{ij}\right]$ are two matrices of same order, say $m\times n$ , then sum or difference of two matrices is defined as matrix $\text{C}={\left[c_{ij}\right]}_{m\times n}$ , where $c_{ij}=a_{ij}+b_{ij}$ , for all possible values of $i\text{ and }j$ .

Apply it,

  $\begin{array}{c}\left[\begin{array}{ll}7\hfill & -12\hfill \\ 15\hfill & 4\hfill \end{array}\right]-\left[\begin{array}{ll}9\hfill & 6\hfill \\ 4\hfill & -9\hfill \end{array}\right]=\left[\begin{array}{ll}7-9\hfill & -12-6\hfill \\ 15-4\hfill & 4-\left(-9\right)\hfill \end{array}\right]\\ =\left[\begin{array}{ll}-2\hfill & -18\hfill \\ 11\hfill & 13\hfill \end{array}\right]\end{array}$

Thus, the value of matrix is $\left[\begin{array}{ll}-2\hfill & -18\hfill \\ 11\hfill & 13\hfill \end{array}\right]$ .