2. IF'A = ( ) and B = ( ), find (24)" + B". 3 -4 2. If A = ( 5 -2 7 3 -9), find (2A)" + B". 1 | 3. Consider the polynomials 7 = -t² + t + 15 and s = t2 – t – 15. Compute (7, s).
2. IF'A = ( ) and B = ( ), find (24)" + B". 3 -4 2. If A = ( 5 -2 7 3 -9), find (2A)" + B". 1 | 3. Consider the polynomials 7 = -t² + t + 15 and s = t2 – t – 15. Compute (7, s).
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
Topic Video
Question
Please answer question 2 with details on how to do it.
Thank you.
![---
### Linear Algebra and Polynomial Exercises
#### Problem 2
Given the matrices:
\[ A = \begin{pmatrix} 3 & -4 & 1 \\ 5 & 2 & 6 \end{pmatrix} \]
\[ B = \begin{pmatrix} -2 & 7 & 5 \\ 1 & 3 & -9 \end{pmatrix} \]
Find \((2A)^T + B^T\).
#### Problem 3
Consider the polynomials:
\[
\vec{r} = -t^2 + t + 15
\]
\[
\vec{s} = t^2 - t - 15
\]
Compute \(\langle \vec{r}, \vec{s} \rangle\).
---
### Solution Explanation
While working with these problems:
1. First, compute the transpose of \(2A\) and \(B\).
2. Then add the resulting matrices.
3. For the polynomials, you will need to use the definition of the inner product (dot product) for polynomials.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1296c196-158c-4a2c-9587-82b5996e9fed%2Fbdfd04b4-3a37-46a8-84cf-84b8ebab1f9b%2Fp474faf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Linear Algebra and Polynomial Exercises
#### Problem 2
Given the matrices:
\[ A = \begin{pmatrix} 3 & -4 & 1 \\ 5 & 2 & 6 \end{pmatrix} \]
\[ B = \begin{pmatrix} -2 & 7 & 5 \\ 1 & 3 & -9 \end{pmatrix} \]
Find \((2A)^T + B^T\).
#### Problem 3
Consider the polynomials:
\[
\vec{r} = -t^2 + t + 15
\]
\[
\vec{s} = t^2 - t - 15
\]
Compute \(\langle \vec{r}, \vec{s} \rangle\).
---
### Solution Explanation
While working with these problems:
1. First, compute the transpose of \(2A\) and \(B\).
2. Then add the resulting matrices.
3. For the polynomials, you will need to use the definition of the inner product (dot product) for polynomials.
---
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 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.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