Which of the following is a basis for P3 (R) when viewed as a vector space over R with the usual vector space operations? [Hint: Use what we learned this week and you can greatly reduce the number of options. For those that remain, take a close look - you will not need to row reduce.] O a. {a2 + 2x, 2x³ + x + 1, x³ + x² – x + 1, 2x + 1} O b. {x³ + x, x³ – a², x³ + 1} O c. {x³ + 2x² + 3x + 4, 4a³ + 3x² + 2x + 1, x³ – x² + x – 1} O d. {x² + x – 1, 2x? + 2x – 2, x³ + x + 4, 8} O e. {9x³ + x² + x, 4x³ + 4x? + 2, 11a + 7, x2 – x, x² + x} O f. {1, x + 1, x² + 2x + 1, x³ + 3x² + 3x + 1, 4x³ + 3x² + 2x + 1} g. {x³ + x, x³ – 1, 2a3 + * – 1, a² +1} O h. {x² + 4x – 3, x' + 7x – 1, –g³ + 4a² + 3x + 9, 8x + 7, r³ – 7} O i. {r* +a + 1, a° +x² + 1, z° + x² + æ} i.
Which of the following is a basis for P3 (R) when viewed as a vector space over R with the usual vector space operations? [Hint: Use what we learned this week and you can greatly reduce the number of options. For those that remain, take a close look - you will not need to row reduce.] O a. {a2 + 2x, 2x³ + x + 1, x³ + x² – x + 1, 2x + 1} O b. {x³ + x, x³ – a², x³ + 1} O c. {x³ + 2x² + 3x + 4, 4a³ + 3x² + 2x + 1, x³ – x² + x – 1} O d. {x² + x – 1, 2x? + 2x – 2, x³ + x + 4, 8} O e. {9x³ + x² + x, 4x³ + 4x? + 2, 11a + 7, x2 – x, x² + x} O f. {1, x + 1, x² + 2x + 1, x³ + 3x² + 3x + 1, 4x³ + 3x² + 2x + 1} g. {x³ + x, x³ – 1, 2a3 + * – 1, a² +1} O h. {x² + 4x – 3, x' + 7x – 1, –g³ + 4a² + 3x + 9, 8x + 7, r³ – 7} O i. {r* +a + 1, a° +x² + 1, z° + x² + æ} i.
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
just an answer no need for explanation
![Which of the following is a basis for P3 (R) when viewed as a vector space over R with the usual vector space
operations?
[Hint: Use what we learned this week and you can greatly reduce the number of options. For those that
remain, take a close look - you will not need to row reduce.]
{x? + 2x, 2x3 + x + 1, x³ + x² – x + 1, 2x + 1}
a.
b. {x³ + x, x³ – x², x³ + 1}
{x³ + 2x? + 3x + 4, 4x3 + 3x? + 2x + 1, a – æ² + x – 1}
C.
d. {x2 + x – 1, 2x2 + 2x – 2, x³ + x + 4, 8}
-
{9x³ + x? + x, 4x³ + 4x² + 2, 1lx + 7, x² – x, ² + x}
е.
-
f. {1,
x + 1, x? + 2x + 1, x³ + 3x? + 3x + 1, 4x3 + 3x? + 2x + 1}
g.
{x³ + x, x³ – 1, 2a + x – 1, x² + 1}
-
h. {x? + 4x – 3, x³ + 7x – 1, –x³ + 4x? + 3x + 9, 8x + 7, x³ – 7}
--
-
O i. {r³ + x + 1, x³ + x² + 1, x³ + x² + x}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4703214b-7b6d-48dc-8fec-73bc2badaa48%2Fdca9cf5c-eedb-47e0-8f91-a9273139909a%2Fhcfxhx_processed.png&w=3840&q=75)
Transcribed Image Text:Which of the following is a basis for P3 (R) when viewed as a vector space over R with the usual vector space
operations?
[Hint: Use what we learned this week and you can greatly reduce the number of options. For those that
remain, take a close look - you will not need to row reduce.]
{x? + 2x, 2x3 + x + 1, x³ + x² – x + 1, 2x + 1}
a.
b. {x³ + x, x³ – x², x³ + 1}
{x³ + 2x? + 3x + 4, 4x3 + 3x? + 2x + 1, a – æ² + x – 1}
C.
d. {x2 + x – 1, 2x2 + 2x – 2, x³ + x + 4, 8}
-
{9x³ + x? + x, 4x³ + 4x² + 2, 1lx + 7, x² – x, ² + x}
е.
-
f. {1,
x + 1, x? + 2x + 1, x³ + 3x? + 3x + 1, 4x3 + 3x? + 2x + 1}
g.
{x³ + x, x³ – 1, 2a + x – 1, x² + 1}
-
h. {x? + 4x – 3, x³ + 7x – 1, –x³ + 4x? + 3x + 9, 8x + 7, x³ – 7}
--
-
O i. {r³ + x + 1, x³ + x² + 1, x³ + x² + x}
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