Chapter 16.1, Problem 18OE

To determine

To describe: the zero matrices from the given matrices.

Answer to Problem 18OE

The zero matrix is $\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$ .

Explanation of Solution

Given information:

Given matrices are,

  $\left[\begin{array}{ccc}9& 2& -4\\ 3& \frac{1}{2}& 6\end{array}\right]$ , $\left[\begin{array}{cc}4& 1\\ 6& 0\\ 9& -4\end{array}\right]$ , $\left[\begin{array}{c}12\end{array}\right]$ , $\left[\begin{array}{c}6\\ 0\\ -8\\ 1\end{array}\right]$ , $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ , $\left[\begin{array}{ccccc}4& 9& -3& 0& 2\end{array}\right]$ , $\left[\begin{array}{c}4\\ -5\\ 3\\ 14\end{array}\right]$ , and $\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$

Calculation:

Consider the given matrices.

  $\left[\begin{array}{ccc}9& 2& -4\\ 3& \frac{1}{2}& 6\end{array}\right]$ , $\left[\begin{array}{cc}4& 1\\ 6& 0\\ 9& -4\end{array}\right]$ , $\left[\begin{array}{c}12\end{array}\right]$ , $\left[\begin{array}{c}6\\ 0\\ -8\\ 1\end{array}\right]$ , $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ , $\left[\begin{array}{ccccc}4& 9& -3& 0& 2\end{array}\right]$ , $\left[\begin{array}{c}4\\ -5\\ 3\\ 14\end{array}\right]$ , and $\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$

A zero matrix should have all elements as zero.

In the matrix $\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$ , all elements are zero.

Therefore, $\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$ is the only zero matrix.