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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 12
Chapter 6, Problem 12

Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.
∣−9∣\(\begin{vmatrix}\)-9\(\end{vmatrix}\)

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1
Identify the number of rows and columns in the given matrix. Since it is a 1x1 matrix, it has 1 row and 1 column.
Express the dimension of the matrix as \$1 \(\times\) 1\$, where the first number represents the number of rows and the second number represents the number of columns.
Determine if the matrix is a square matrix. A square matrix has the same number of rows and columns. Since this matrix is 1x1, it is a square matrix.
Check if the matrix is a row matrix. A row matrix has exactly one row and multiple columns. Since this matrix has only one column, it is not a row matrix.
Check if the matrix is a column matrix. A column matrix has exactly one column and multiple rows. Since this matrix has only one row, 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 2×3 matrix has 2 rows and 3 columns. Understanding dimensions helps classify matrices and perform operations correctly.
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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 cases are useful in vector representation and simplify certain matrix operations.
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Related Practice
Textbook Question

Solve each system by substitution.

7x - y = -10

3y - x = 10

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Textbook Question

Graph each inequality. x + 2y ≤ 6

Textbook Question

Find the values of the variables for which each statement is true, if possible.

[−3ab5]=[c04d]\(\left\)[ \(\begin{matrix}\) -3 & a \\ b & 5 \(\end{matrix}\) \(\right\)] = \(\left\)[ \(\begin{matrix}\) c & 0 \\ 4 & d \(\end{matrix}\) \(\right\)]

Textbook Question

Solve each system by substitution.

8x - 10y = -22

3x + y = 6

Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices.

[24]\(\left\)[ \(\begin{matrix}\) 2 \\ 4 \(\end{matrix}\) \(\right\)]

Textbook Question

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

[01000−21−10]and[1011000−10]\(\left\)[ \(\begin{matrix}\) 0 & 1 & 0 \\0 & 0 & -2 \\1 & -1 & 0 \(\end{matrix}\) \(\right\)]\(\quad\) \(\text{and}\) \(\quad\]\left\)[ \(\begin{matrix}\) 1 & 0 & 1 \\1 & 0 & 0 \\0 & -1 & 0 \(\end{matrix}\) \(\right\)]