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Chapter 9: Problem 10

Determine the size of each matrix. \(\left[\begin{array}{r}-3 \\ y \\ 5\end{array}\right]\)

Short Answer

Expert verified
3 x 1

Step by step solution

01

Identify the Rows

Count the number of horizontal entities in the matrix. The provided matrix has 3 entries arranged vertically.
02

Identify the Columns

Next, count the number of vertical entities. The matrix has a single column since all entries are aligned in one vertical line.
03

Determine the Size

The size of a matrix is given in the format of Rows x Columns. From the previous steps, there are 3 rows and 1 column.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Matrix Dimensions
Understanding the dimensions of a matrix is crucial.
The dimensions indicate the number of rows and columns.
The size of a matrix is typically represented as Rows x Columns.
This format helps in identifying how many elements are arranged horizontally (rows) and vertically (columns).
For example, a matrix with 3 rows and 1 column is denoted as a 3x1 matrix.
Rows and Columns
Matrices are organized into rows and columns.
Rows are horizontal lines of elements, while columns are vertical lines.
To determine the number of rows, count the entities horizontally.
For columns, count the entities vertically.
In our matrix, we observe the following:
  • 3 rows: because there are three levels of entries (-3, y, 5)
  • 1 column: because all entries are in one vertical line
By counting these, we accurately determine the matrix size.
Matrix Identification
Matrix identification involves understanding the structure and layout of matrix elements.
Given the matrix \(\left[\begin{array}{r}-3 \ y \ 5\end{array}\right]\), we can see the following:
  • Each element is aligned in a single column
  • The elements are placed in three separate rows
Therefore, we identify this as a 3x1 matrix based on its rows and columns.
This format helps in further matrix operations like addition, multiplication, and finding inverses.

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