Chapter 4, Problem 6STP

To determine

Tofind:the dimension of the matrix $\text{D}$ .

Answer to Problem 6STP

The option $\text{F}$ is correct option: the dimension of matrices of $\text{D}$ is $4\times 2$ .

Explanation of Solution

Given:

  $\text{A=}\left[\begin{array}{c}4\\ \text{-5}\\ -3\end{array}\begin{array}{c}3\\ \text{1}\\ 7\end{array}\right]$ , $\text{B=}\left[\begin{array}{ccc}1& -9& 2\\ 0& 10& 4\end{array}\right]$ .

Concept used:

The number of rows and the columns that a matrix has is called dimension or its order denoted by $\text{row}\times \text{column}$ .

Dimension of the matrix:

  $\text{row}\times \text{column}$ .

Calculation:

  $\text{D=}\left[\begin{array}{cc}\text{4}& \text{-6}\\ \text{9}& \text{2}\\ \text{1}& \text{0}\\ \text{-3}& \text{-5}\end{array}\right]$ .

  ${\text{a}}_{\text{11}}$ = position number one first row and first column. So, the two digits number below shows the position of the row and the column specifically first digit from the left shows the rows and second digit shows column.

The number of rows and the columns that a matrix has is called dimension or its order denoted by $\text{row}\times \text{column}$ .

Since, the given matrices $\text{D}$ has 4 row and 2 columns and dimensions are denoted as $\text{row×column}$ .

The dimension of matrices of $\text{D}$ is $4\times 2$ .

Hence, option $\text{F}$ is correct option.