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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 11
Chapter 6, Problem 11

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

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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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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 1×2 matrix has 1 row and 2 columns. Understanding dimensions helps in identifying the size and structure of the matrix.
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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 special 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 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.
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Related Practice
Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. x/(x2 + 4x - 5)

Textbook Question

Graph each inequality. x + 2y ≤ 6

Textbook Question

Evaluate each determinant.

∣93−3−1∣\(\left\)| \(\begin{matrix}\) 9 & 3 \\ -3 & -1 \(\end{matrix}\) \(\right\)|

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Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.

∣−9∣\(\begin{vmatrix}\)-9\(\end{vmatrix}\)

Textbook Question

Solve each system by substitution.

8x - 10y = -22

3x + y = 6

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.

y = 3x2

x2 + y2 = 10

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