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
![The image contains two matrices, \([G]\) and \([B]\), along with an expression involving these matrices. The task is to calculate \(3[G] + 4[B]\).
**Matrix \([G]\):**
\[
[G] = \begin{bmatrix}
-3 & -2 & 0 & 10 & 0 & 0 \\
-5 & -9 & -5 & -6 & 4 & 0 \\
3 & -8 & -6 & 1 & -2 & 0 \\
3 & 9 & 1 & -10 & 2 & 0 \\
4 & 9 & 6 & 2 & 5 & 0 \\
\end{bmatrix}
\]
**Matrix \([B]\):**
\[
[B] = \begin{bmatrix}
-8 & 4 & -8 & 8 & 10 \\
7 & -5 & -4 & 2 & 3 \\
10 & -3 & 1 & 4 & 8 \\
9 & -6 & -3 & 7 & 2 \\
-5 & -1 & 1 & 3 & 0 \\
\end{bmatrix}
\]
**Expression:**
\[
3[G] + 4[B] =
\begin{bmatrix}
\text{(blank spaces for the result)}
\end{bmatrix}
\]
### Explanation
The expression requires the scalar multiplication of matrix \([G]\) by 3 and matrix \([B]\) by 4, followed by the addition of the two resulting matrices. The blank matrix indicates where the results of this calculation will be inserted, containing 5 rows and 5 columns to match the dimensions of both \([G]\) and \([B]\). Each element in the resulting matrix is computed by multiplying the corresponding element from \([G]\) by 3 and \([B]\) by 4, then summing these products.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd73810a-c249-4a89-b8c9-68bba5fd26a7%2F860eaa77-9e32-42bc-8f6b-adfbf20c9088%2F3yp1xb_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains two matrices, \([G]\) and \([B]\), along with an expression involving these matrices. The task is to calculate \(3[G] + 4[B]\).
**Matrix \([G]\):**
\[
[G] = \begin{bmatrix}
-3 & -2 & 0 & 10 & 0 & 0 \\
-5 & -9 & -5 & -6 & 4 & 0 \\
3 & -8 & -6 & 1 & -2 & 0 \\
3 & 9 & 1 & -10 & 2 & 0 \\
4 & 9 & 6 & 2 & 5 & 0 \\
\end{bmatrix}
\]
**Matrix \([B]\):**
\[
[B] = \begin{bmatrix}
-8 & 4 & -8 & 8 & 10 \\
7 & -5 & -4 & 2 & 3 \\
10 & -3 & 1 & 4 & 8 \\
9 & -6 & -3 & 7 & 2 \\
-5 & -1 & 1 & 3 & 0 \\
\end{bmatrix}
\]
**Expression:**
\[
3[G] + 4[B] =
\begin{bmatrix}
\text{(blank spaces for the result)}
\end{bmatrix}
\]
### Explanation
The expression requires the scalar multiplication of matrix \([G]\) by 3 and matrix \([B]\) by 4, followed by the addition of the two resulting matrices. The blank matrix indicates where the results of this calculation will be inserted, containing 5 rows and 5 columns to match the dimensions of both \([G]\) and \([B]\). Each element in the resulting matrix is computed by multiplying the corresponding element from \([G]\) by 3 and \([B]\) by 4, then summing these products.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
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