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,...
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Question
Please go through each option with explanation
![Consider the vector space P3 of polynomials of degree at most 2.
Some of the statements about the polynomials
x – 1
x+ 2
x? + 3
are correct and some are incorrect. Select the correct statements.
If we remove the third polynomial from the list, the remaining two polynomials
x – 1
x+ 2
span a 1-dimensional subspace of P3.
| These three polynomials are linearly independent because the only zero linear
combination of the three is when all three coefficients are 0.
) These three polynomial are a spanning set for P3.
| These three polynomials are linearly independent because there are three of them and
dim(P3)=3
| These three polynomials are linearly dependent because two of them are first order
polynomials.
If we remove the third polynomial from the list, the remaining two polynomials
x – 1
x + 2
span a 2-dimensional subspace of P3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7ecf9f2-18d9-4a63-a715-89d962230eda%2F1f3d5cfd-6a29-4dfb-bdb2-63e5a70c3328%2Fzhcaebv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the vector space P3 of polynomials of degree at most 2.
Some of the statements about the polynomials
x – 1
x+ 2
x? + 3
are correct and some are incorrect. Select the correct statements.
If we remove the third polynomial from the list, the remaining two polynomials
x – 1
x+ 2
span a 1-dimensional subspace of P3.
| These three polynomials are linearly independent because the only zero linear
combination of the three is when all three coefficients are 0.
) These three polynomial are a spanning set for P3.
| These three polynomials are linearly independent because there are three of them and
dim(P3)=3
| These three polynomials are linearly dependent because two of them are first order
polynomials.
If we remove the third polynomial from the list, the remaining two polynomials
x – 1
x + 2
span a 2-dimensional subspace of P3
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