Chapter 4.1, Problem 1ACYP

To determine

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

Answer to Problem 1ACYP

The dimension of $\text{B}$ is $\text{3}\times 2$ .

Explanation of Solution

Given:

  $\text{B=}\left[\begin{array}{c}\text{10}\\ \text{-2}\\ \text{6}\end{array}\begin{array}{c}\text{-8}\\ \text{19}\\ \text{-1}\end{array}\right]$

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:

  $\text{B=}\left[\begin{array}{c}\text{10}\\ \text{-2}\\ \text{6}\end{array}\begin{array}{c}\text{-8}\\ \text{19}\\ \text{-1}\end{array}\right]$ .

  $\text{B=}\left[\begin{array}{c}{a}_{11}\\ {\text{a}}_{21}\\ {\text{a}}_{31}\end{array}\begin{array}{c}{\text{a}}_{12}\\ {\text{a}}_{22}\\ {\text{a}}_{32}\end{array}\right]$ .

  ${\text{a}}_{\text{11}}$ = position number one first row and first column. So the two digit number below the a 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.

Since, the $\text{B}$ matrices havetotal of 3 rows and 2 columns.

Hence, the dimension of $\text{B}$ is $\text{3}\times 2$ .