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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 9
Chapter 6, Problem 9

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 \(\end{matrix}\) \(\right\)]

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1
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.
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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.
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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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Related Practice
Textbook Question

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary.

6x + 10y = -11

9x + 6y = -3

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Textbook Question

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations.

2x2 = 3y + 23

y = 2x - 5

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Textbook Question

Evaluate each determinant.

∣−1−253∣\(\left\)| \(\begin{matrix}\) -1 & -2 \\ 5 & 3 \(\end{matrix}\) \(\right\)|

Textbook Question

Use the given row transformation to change each matrix as indicated.

[156−23−1470],2×row 1 added to row 2\(\left\)[ \(\begin{matrix}\) 1 & 5 & 6 \\ -2 & 3 & -1 \\ 4 & 7 & 0 \(\end{matrix}\) \(\right\)], \(\quad\) 2 \(\times\) \(\text{row 1 added to row 2}\)

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Textbook Question

Use the given row transformation to change each matrix as indicated.

[1−470],−7×row 1 added to row 2\(\left\)[ \(\begin{matrix}\) 1 & -4 \\ 7 & 0 \(\end{matrix}\) \(\right\)], \(\quad\) -7 \(\times\) \(\text{row 1 added to row 2}\)

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x + 2)/((x + 2)(2x - 1))

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