Find the dimension of each matrix. Identify any square, column, or row matrices. [−680041923−571]\left[ \begin{matrix} -6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \\ 3 & -5 & 7 & 1 \end{matrix} \right]

Ch. 5 - Systems and Matrices

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 9

Chapter 6, Problem 9

Find the dimension of each matrix. Identify any square, column, or row matrices.
$[\begin{matrix} - 6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \\ 3 & - 5 & 7 & 1 \end{matrix}]$

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Recall that the dimension of a matrix is given by the number of rows and columns it has, usually written as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

To find the dimension of each matrix, count the number of horizontal entries (rows) and the number of vertical entries (columns) in the matrix.

Identify if the matrix is a square matrix by checking if the number of rows equals the number of columns, i.e., if $m = n$, then the matrix is square.

Check if the matrix is a column matrix by seeing if it has exactly one column, i.e., if $n = 1$, then it is a column matrix.

Check if the matrix is a row matrix by seeing if it has exactly one row, i.e., if $m = 1$, then it is a row matrix.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 the dimension 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 consists of a single row with multiple columns (1×n), while a column matrix has a single column with multiple rows (m×1). Recognizing these helps in understanding matrix structure and is useful in vector representation and matrix multiplication.

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