Skip to main content
Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblem 14b
Chapter 7, Problem 14b

In Exercises 9 - 16, find the following matrices: b. A - B
Matrices A and B for exercise 14 in college algebra, showing A = [6 2 -3] and B = [4 -2 3].

Verified step by step guidance
1
Step 1: Identify the matrices A and B. Here, A = [6 2 -3] and B = [4 -2 3]. Both are 1x3 matrices (row vectors).
Step 2: Understand that matrix subtraction A - B is performed by subtracting corresponding elements of B from A.
Step 3: Set up the subtraction element-wise: (6 - 4), (2 - (-2)), and (-3 - 3).
Step 4: Perform each subtraction separately: 6 - 4, 2 - (-2), and -3 - 3, but do not calculate the final values yet.
Step 5: Write the resulting matrix as [6 - 4, 2 - (-2), -3 - 3], which represents the matrix A - B.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

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

Matrix Representation

A matrix is a rectangular array of numbers arranged in rows and columns. In this problem, matrices A and B are 1x3 row matrices, meaning they each have one row and three columns. Understanding the structure of matrices is essential for performing operations like addition or subtraction.
Recommended video:
Guided course
8:38
Performing Row Operations on Matrices

Matrix Subtraction

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions. For matrices A and B, each element in A is subtracted by the corresponding element in B to form a new matrix. This operation is only defined when both matrices have identical dimensions.
Recommended video:
5:56
Adding & Subtracting Functions

Element-wise Operations

Element-wise operations apply arithmetic operations to each corresponding element in matrices. For subtraction, this means subtracting each element in matrix B from the corresponding element in matrix A individually. This concept ensures clarity in performing matrix operations correctly.
Recommended video:
Guided course
8:38
Performing Row Operations on Matrices
Related Practice
Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4A

1
views
Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. {4x−5y=172x+3y=3\(\begin{cases}\)4x - 5y = 17 \\2x + 3y = 3\(\end{cases}\)

Textbook Question

Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D

A=[2−1253−1]B=[0−2321−5]C=[123−112−121]D=[−2313−24]A=\(\begin{bmatrix}\)2 & -1 & 2\\ 5 & 3 & -1\(\end{bmatrix}\[\quad\) B=\(\begin{bmatrix}\)0 & -2\\ 3 & 2\\ 1 & -5\(\end{bmatrix}\)C=\(\begin{bmatrix}\)1 & 2 & 3\\ -1 & 1 & 2\\ -1 & 2 & 1\(\end{bmatrix}\]\quad\) D=\(\begin{bmatrix}\)-2 & 3 & 1\\ 3 & -2 & 4\(\end{bmatrix}\)

1
views
Textbook Question

In Exercises 9 - 16, find the following matrices: a. A + B

1
views