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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 10
Chapter 6, Problem 10

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

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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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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 5×1 matrix has 5 rows and 1 column. 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 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 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.
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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

Solve each system by substitution.

x - 5y = 8

x = 6y

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Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix In.)

[5723]and[3−7−25]\(\left\)[ \(\begin{matrix}\) 5 & 7 \\2 & 3 \(\end{matrix}\) \(\right\)]\(\quad\) \(\text{and}\) \(\quad\]\left\)[ \(\begin{matrix}\) 3 & -7 \\-2 & 5 \(\end{matrix}\) \(\right\)]

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Textbook Question

Evaluate each determinant.

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

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Textbook Question

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

[156−4−12371],4×row 1 added to row 2\(\left\)[ \(\begin{matrix}\) 1 & 5 & 6 \\ -4 & -1 & 2 \\ 3 & 7 & 1 \(\end{matrix}\) \(\right\)], \(\quad\) 4 \(\times\) \(\text{row 1 added to row 2}\)

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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.

y = 3x2

x2 + y2 = 10

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