Find the dimension of each matrix. Identify any square, column, or row matrices. [−4823]\left[ \begin{matrix} -4 & 8 \\ 2 & 3 \end{matrix} \right]

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 7

6장, 문제 7

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

검증된 단계별 안내

Step 1: Understand that the dimension of a matrix is given by the number of rows and columns it contains, usually written as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

Step 2: Count the number of rows in the matrix. Each horizontal line of elements represents one row.

Step 3: Count the number of columns in the matrix. Each vertical line of elements represents one column.

Step 4: Write the dimension as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

Step 5: Identify the type of matrix based on its dimensions: if $m = n$, it is a square matrix; if $n = 1$, it is a column matrix; if $m = 1$, it is a row matrix.

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주요 개념

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Matrix Dimension

The dimension of a matrix is described by the number of its rows and columns, written as 'rows × columns'. For example, a matrix with 3 rows and 4 columns has a dimension of 3×4. Understanding dimensions is essential for identifying matrix types and performing operations.

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). Recognizing these helps in understanding matrix structure and is useful in vector representation and matrix multiplication.

Find the dimension of each matrix. Identify any square, column, or row matrices. [−4823]\(\left\)[ \(\begin{matrix}\) -4 & 8 \\ 2 & 3 \(\end{matrix}\) \(\right\)]