Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![Let
\( A = \begin{bmatrix} 4 & 0 \\ -1 & 6 \end{bmatrix} \), \( D = \begin{bmatrix} 0 & -4 \\ -2 & 1 \end{bmatrix} \).
Compute the indicated matrix. (If this is not possible, enter DNE in any single blank).
\[ A + 2D \]
The task is to calculate the matrix resulting from the expression \( A + 2D \).
1. First, calculate \( 2D \) by multiplying each element of the matrix \( D \) by 2:
\[
2D = \begin{bmatrix} 0 \times 2 & -4 \times 2 \\ -2 \times 2 & 1 \times 2 \end{bmatrix} = \begin{bmatrix} 0 & -8 \\ -4 & 2 \end{bmatrix}
\]
2. Next, add matrix \( A \) and matrix \( 2D \):
\[
A + 2D = \begin{bmatrix} 4 & 0 \\ -1 & 6 \end{bmatrix} + \begin{bmatrix} 0 & -8 \\ -4 & 2 \end{bmatrix} = \begin{bmatrix} 4+0 & 0-8 \\ -1-4 & 6+2 \end{bmatrix} = \begin{bmatrix} 4 & -8 \\ -5 & 8 \end{bmatrix}
\]
3. Enter the resulting values into the matrix brackets provided in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b2b33db-c80f-4b0b-994f-adea14a053ac%2Fb05ea43a-cdb7-45af-ba33-382dbc2c1bf6%2F6a3o6346_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let
\( A = \begin{bmatrix} 4 & 0 \\ -1 & 6 \end{bmatrix} \), \( D = \begin{bmatrix} 0 & -4 \\ -2 & 1 \end{bmatrix} \).
Compute the indicated matrix. (If this is not possible, enter DNE in any single blank).
\[ A + 2D \]
The task is to calculate the matrix resulting from the expression \( A + 2D \).
1. First, calculate \( 2D \) by multiplying each element of the matrix \( D \) by 2:
\[
2D = \begin{bmatrix} 0 \times 2 & -4 \times 2 \\ -2 \times 2 & 1 \times 2 \end{bmatrix} = \begin{bmatrix} 0 & -8 \\ -4 & 2 \end{bmatrix}
\]
2. Next, add matrix \( A \) and matrix \( 2D \):
\[
A + 2D = \begin{bmatrix} 4 & 0 \\ -1 & 6 \end{bmatrix} + \begin{bmatrix} 0 & -8 \\ -4 & 2 \end{bmatrix} = \begin{bmatrix} 4+0 & 0-8 \\ -1-4 & 6+2 \end{bmatrix} = \begin{bmatrix} 4 & -8 \\ -5 & 8 \end{bmatrix}
\]
3. Enter the resulting values into the matrix brackets provided in the image.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education