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 14a
Chapter 7, Problem 14a

In Exercises 9 - 16, find the following matrices: a. A + B
Matrices A and B for exercise 14 in college algebra, chapter on systems of equations.

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 (one row, three columns).
Step 2: Understand that matrix addition requires matrices to be of the same dimension. Since both A and B are 1x3, we can add them element-wise.
Step 3: Add the corresponding elements of matrices A and B: add the first elements (6 + 4), the second elements (2 + (-2)), and the third elements (-3 + 3).
Step 4: Write the resulting matrix from the sums of each corresponding element to get A + B.
Step 5: Express the final matrix as a 1x3 matrix with the sums calculated in the previous step.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

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

Matrix Addition

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Each element in the resulting matrix is the sum of elements in the same position from the original matrices. For example, if A and B are both 1x3 matrices, then (A + B) is also a 1x3 matrix where each element is A[i] + B[i].
Recommended video:
Guided course
8:38
Performing Row Operations on Matrices

Matrix Dimensions and Compatibility

To add two matrices, they must have the same dimensions, meaning the same number of rows and columns. If matrices differ in size, addition is undefined. In this problem, both A and B are 1x3 matrices, so addition is possible and straightforward.
Recommended video:
Guided course
4:35
Introduction to Matrices

Representation of Matrices

Matrices are rectangular arrays of numbers arranged in rows and columns. They can represent data or systems of equations. Understanding how to read and write matrices, such as A = [6 2 -3], is essential for performing operations like addition or multiplication.
Recommended video:
Guided course
4:35
Introduction to 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: b. A - B

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

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: c. - 4A