Find the dimension of each matrix. Identify any square, column, or row matrices. [8−2463]\left[ \begin{matrix} 8 & -2 & 4 & 6 & 3 \end{matrix} \right]

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 10

6장, 문제 10

Find the dimension of each matrix. Identify any square, column, or row matrices.
$[\begin{matrix} 8 & - 2 & 4 & 6 & 3 \end{matrix}]$

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Understand that the dimension of a matrix is given by the number of rows multiplied by the number of columns, written as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

Given the matrix is described as a $5 \times 1$ matrix, this means it has 5 rows and 1 column.

Write down the dimension explicitly as $5 \times 1$.

Identify the type of matrix based on its dimensions: since it has only one column, it is a column matrix.

Note that it is not a square matrix because the number of rows (5) is not equal to the number of columns (1), and it is not a row matrix because it has more than one row.

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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 5×1 matrix has 5 rows and 1 column. 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 unique 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). These special forms are useful in vector representation and simplify certain matrix operations.

Find the dimension of each matrix. Identify any square, column, or row matrices. [8−2463]\(\left\)[ \(\begin{matrix}\) 8 & -2 & 4 & 6 & 3 \(\end{matrix}\) \(\right\)]