Chapter 8.1, Problem 31E

To determine

To fill: the blank in the given matrix

Answer to Problem 31E

Missing element is 2

Explanation of Solution

Given information:

The given matrices are

  $\left[\begin{array}{ccc}3& 6& 8\\ 4& -3& 6\end{array}\right]$ and $\left[\begin{array}{ccc}1& & \frac{8}{3}\\ 4& -3& 6\end{array}\right]$

Calculation:

Consider the following matrices,

  $\left[\begin{array}{ccc}3& 6& 8\\ 4& -3& 6\end{array}\right]$ ................(1)

  $\left[\begin{array}{ccc}1& & \frac{8}{3}\\ 4& -3& 6\end{array}\right]$ .....................(2)

Here second row of these matrices are same and given elements of first row in the matrix (2) are one third of that of matrix (1).

Therefore to convert matrix (1) into matrix (2) use following row operation,

Multiply first row of matrix (1) by $\frac{1}{3}$ ,

That is,

  $\left[\begin{array}{ccc}1& 2& \frac{8}{3}\\ 4& -3& 6\end{array}\right]$

Hence missing element is 2.