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Chapter 4: Problem 13

Determine the size of each matrix. $$ \left[\begin{array}{l} 1 \\ 0 \end{array}\right] $$

Short Answer

Expert verified
The matrix size is 2 脳 1.

Step by step solution

01

Identify Rows and Columns

To determine the size of the matrix, first identify the number of rows and columns it has.
02

Count the Rows

Count the number of horizontal elements present. In this case, the matrix has 2 rows.
03

Count the Columns

Count the number of vertical elements present. Here, there is only 1 column.
04

State the Size

Combine the number of rows and columns in the format (rows 脳 columns).

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Key Concepts

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

Matrix Rows
When determining the size of a matrix, one must first count the rows. Rows are the horizontal lines of elements in a matrix. They are crucial for knowing how many separate levels or stages the matrix has.
For example, in the matrix:
\[\begin{bmatrix} 1 \ 0 \ \end{bmatrix}\]
We see two elements arranged horizontally, so this matrix has 2 rows.

Identifying rows is essential for various operations on matrices, including addition, subtraction, and multiplication.
Matrix Columns
Columns in a matrix are just as important as rows. A column is a vertical line of elements. To discover the total number of columns, look at the matrix vertically.
In our example:
\[\begin{bmatrix} 1 \ 0 \ \end{bmatrix}\]
We have one vertical line of elements, meaning there is only 1 column.

Columns help determine the matrix structure, which is vital in processes like matrix-vector multiplication and solving systems of linear equations.
Matrix Dimensions
The dimensions of a matrix are a combination of its rows and columns. We express these dimensions in the format (rows 脳 columns).
For example, from our previous matrix:
\[\begin{bmatrix} 1 \ 0 \ \end{bmatrix}\]
We found that it has 2 rows and 1 column. Hence, its dimensions are given as 2 脳 1.

Understanding matrix dimensions is fundamental for performing matrix operations and ensuring conformability in linear algebra applications. Proper understanding of matrix dimensions ensures smooth progression through matrix manipulations and aids in effectively solving mathematical and real-world problems involving matrices.

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Most popular questions from this chapter

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