Find the dimension of each matrix. Identify any square, column, or row matrices. [24]\left[ \begin{matrix} 2 \\ 4 \end{matrix} \right]

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 11

6장, 문제 11

Find the dimension of each matrix. Identify any square, column, or row matrices.
$[\begin{matrix} 2 \\ 4 \end{matrix}]$

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Identify the number of rows and columns in the given matrix. For a matrix written as 1x2, it means there is 1 row and 2 columns.

Write the dimension of the matrix as the number of rows by the number of columns, which is $1 \times 2$ in this case.

Determine if the matrix is a square matrix by checking if the number of rows equals the number of columns. Since 1 is not equal to 2, this matrix is not square.

Check if the matrix is a row matrix by seeing if it has exactly one row. Since it has 1 row, it is a row matrix.

Check if the matrix is a column matrix by seeing if it has exactly one column. Since it has 2 columns, it is not a column matrix.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Matrix Dimension

The dimension of a matrix is described by the number of its rows and columns, written as 'rows × columns'. For example, a 1×2 matrix has 1 row and 2 columns. Understanding dimensions helps in identifying the size and structure of the matrix.

Square Matrix

A square matrix has the same number of rows and columns (n×n). This property is important because square matrices have special characteristics, such as the possibility of having a determinant and an inverse, which are not defined for non-square matrices.

Row and Column Matrices

A row matrix has only one row and multiple columns (1×n), while a column matrix has one column and multiple rows (m×1). Recognizing these helps in understanding matrix operations and their applications, such as representing vectors in different orientations.

Find the dimension of each matrix. Identify any square, column, or row matrices. [24]\(\left\)[ \(\begin{matrix}\) 2 \\ 4 \(\end{matrix}\) \(\right\)]