SlideShare a Scribd company logo
1 of 1
Download to read offline
Find dimension and a basis of the following vector spaces:
Solution
So all polynomials with roots:-1,1 and 2
So multiples of polynomial: f(x)=(x+1)(x-1)(x-2) which is polynomial of degree 3
But degree must be less than 6
So basis is :B={f(x),xf(x),x^2f(x),x^3f(x)}
So 4 vectors in basis
HEnce dimension =4

More Related Content

More from jibinsh

The energy used in the CaMn cycle for the production of carbohydrate .pdf
The energy used in the CaMn cycle for the production of carbohydrate .pdfThe energy used in the CaMn cycle for the production of carbohydrate .pdf
The energy used in the CaMn cycle for the production of carbohydrate .pdf
jibinsh
 
The CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdf
The CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdfThe CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdf
The CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdf
jibinsh
 
Recent Presidential debates have brought about a series of polls.pdf
Recent Presidential debates have brought about a series of polls.pdfRecent Presidential debates have brought about a series of polls.pdf
Recent Presidential debates have brought about a series of polls.pdf
jibinsh
 
Please give me a custom example code of a complex PovRay Program tha.pdf
Please give me a custom example code of a complex PovRay Program tha.pdfPlease give me a custom example code of a complex PovRay Program tha.pdf
Please give me a custom example code of a complex PovRay Program tha.pdf
jibinsh
 
A)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdf
A)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdfA)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdf
A)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdf
jibinsh
 
JAVAWrite a program that takes a command-line argument representin.pdf
JAVAWrite a program that takes a command-line argument representin.pdfJAVAWrite a program that takes a command-line argument representin.pdf
JAVAWrite a program that takes a command-line argument representin.pdf
jibinsh
 
Im asking for hypothetical data based on health by raceethnicity .pdf
Im asking for hypothetical data based on health by raceethnicity .pdfIm asking for hypothetical data based on health by raceethnicity .pdf
Im asking for hypothetical data based on health by raceethnicity .pdf
jibinsh
 
I have to write a polynomial class linked list program and i do not .pdf
I have to write a polynomial class linked list program and i do not .pdfI have to write a polynomial class linked list program and i do not .pdf
I have to write a polynomial class linked list program and i do not .pdf
jibinsh
 
I need to adjust this Huffman code so that it asks for the user to i.pdf
I need to adjust this Huffman code so that it asks for the user to i.pdfI need to adjust this Huffman code so that it asks for the user to i.pdf
I need to adjust this Huffman code so that it asks for the user to i.pdf
jibinsh
 
I would like help with the question below. I have done a lot of rese.pdf
I would like help with the question below. I have done a lot of rese.pdfI would like help with the question below. I have done a lot of rese.pdf
I would like help with the question below. I have done a lot of rese.pdf
jibinsh
 
How does H. pylori work in attacking the stomach lining What drugs .pdf
How does H. pylori work in attacking the stomach lining What drugs .pdfHow does H. pylori work in attacking the stomach lining What drugs .pdf
How does H. pylori work in attacking the stomach lining What drugs .pdf
jibinsh
 

More from jibinsh (20)

The following expression was simplified incorrectly. In which line er.pdf
The following expression was simplified incorrectly. In which line er.pdfThe following expression was simplified incorrectly. In which line er.pdf
The following expression was simplified incorrectly. In which line er.pdf
 
The energy used in the CaMn cycle for the production of carbohydrate .pdf
The energy used in the CaMn cycle for the production of carbohydrate .pdfThe energy used in the CaMn cycle for the production of carbohydrate .pdf
The energy used in the CaMn cycle for the production of carbohydrate .pdf
 
The CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdf
The CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdfThe CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdf
The CAN-SPAM Acta.   applies to virtually all promotional e-mails,.pdf
 
SensesFor each of the special senses, understand how a stimulus is.pdf
SensesFor each of the special senses, understand how a stimulus is.pdfSensesFor each of the special senses, understand how a stimulus is.pdf
SensesFor each of the special senses, understand how a stimulus is.pdf
 
Recent Presidential debates have brought about a series of polls.pdf
Recent Presidential debates have brought about a series of polls.pdfRecent Presidential debates have brought about a series of polls.pdf
Recent Presidential debates have brought about a series of polls.pdf
 
Quality function deployment (QFD) is a structures approach for integ.pdf
Quality function deployment (QFD) is a structures approach for integ.pdfQuality function deployment (QFD) is a structures approach for integ.pdf
Quality function deployment (QFD) is a structures approach for integ.pdf
 
please send edited code. I have posted this a few times with lots of.pdf
please send edited code. I have posted this a few times with lots of.pdfplease send edited code. I have posted this a few times with lots of.pdf
please send edited code. I have posted this a few times with lots of.pdf
 
Please give me a custom example code of a complex PovRay Program tha.pdf
Please give me a custom example code of a complex PovRay Program tha.pdfPlease give me a custom example code of a complex PovRay Program tha.pdf
Please give me a custom example code of a complex PovRay Program tha.pdf
 
Networking Question What are the key differences between forwarding.pdf
Networking Question What are the key differences between forwarding.pdfNetworking Question What are the key differences between forwarding.pdf
Networking Question What are the key differences between forwarding.pdf
 
Most children with cystic fibrosis have frequent lung infections and.pdf
Most children with cystic fibrosis have frequent lung infections and.pdfMost children with cystic fibrosis have frequent lung infections and.pdf
Most children with cystic fibrosis have frequent lung infections and.pdf
 
A)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdf
A)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdfA)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdf
A)abductionB)deductive reasoningc) inductive reasoningd)a wild.pdf
 
Lipid rafts are associated with which of the following activities re.pdf
Lipid rafts are associated with which of the following activities re.pdfLipid rafts are associated with which of the following activities re.pdf
Lipid rafts are associated with which of the following activities re.pdf
 
JAVAWrite a program that takes a command-line argument representin.pdf
JAVAWrite a program that takes a command-line argument representin.pdfJAVAWrite a program that takes a command-line argument representin.pdf
JAVAWrite a program that takes a command-line argument representin.pdf
 
In culture A, parents have children until they have a boy and a girl.pdf
In culture A, parents have children until they have a boy and a girl.pdfIn culture A, parents have children until they have a boy and a girl.pdf
In culture A, parents have children until they have a boy and a girl.pdf
 
Im asking for hypothetical data based on health by raceethnicity .pdf
Im asking for hypothetical data based on health by raceethnicity .pdfIm asking for hypothetical data based on health by raceethnicity .pdf
Im asking for hypothetical data based on health by raceethnicity .pdf
 
I have to write a polynomial class linked list program and i do not .pdf
I have to write a polynomial class linked list program and i do not .pdfI have to write a polynomial class linked list program and i do not .pdf
I have to write a polynomial class linked list program and i do not .pdf
 
I need to adjust this Huffman code so that it asks for the user to i.pdf
I need to adjust this Huffman code so that it asks for the user to i.pdfI need to adjust this Huffman code so that it asks for the user to i.pdf
I need to adjust this Huffman code so that it asks for the user to i.pdf
 
How many different diploid genotypes are possible for a gene that ex.pdf
How many different diploid genotypes are possible for a gene that ex.pdfHow many different diploid genotypes are possible for a gene that ex.pdf
How many different diploid genotypes are possible for a gene that ex.pdf
 
I would like help with the question below. I have done a lot of rese.pdf
I would like help with the question below. I have done a lot of rese.pdfI would like help with the question below. I have done a lot of rese.pdf
I would like help with the question below. I have done a lot of rese.pdf
 
How does H. pylori work in attacking the stomach lining What drugs .pdf
How does H. pylori work in attacking the stomach lining What drugs .pdfHow does H. pylori work in attacking the stomach lining What drugs .pdf
How does H. pylori work in attacking the stomach lining What drugs .pdf
 

Recently uploaded

Spellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please PractiseSpellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please Practise
AnaAcapella
 

Recently uploaded (20)

Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
 
Wellbeing inclusion and digital dystopias.pptx
Wellbeing inclusion and digital dystopias.pptxWellbeing inclusion and digital dystopias.pptx
Wellbeing inclusion and digital dystopias.pptx
 
Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024
 
REMIFENTANIL: An Ultra short acting opioid.pptx
REMIFENTANIL: An Ultra short acting opioid.pptxREMIFENTANIL: An Ultra short acting opioid.pptx
REMIFENTANIL: An Ultra short acting opioid.pptx
 
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxHMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
 
Spellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please PractiseSpellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please Practise
 
SOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning PresentationSOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning Presentation
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.
 
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
 
Micro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdfMicro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdf
 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...
 
Single or Multiple melodic lines structure
Single or Multiple melodic lines structureSingle or Multiple melodic lines structure
Single or Multiple melodic lines structure
 
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POS
 
This PowerPoint helps students to consider the concept of infinity.
This PowerPoint helps students to consider the concept of infinity.This PowerPoint helps students to consider the concept of infinity.
This PowerPoint helps students to consider the concept of infinity.
 
General Principles of Intellectual Property: Concepts of Intellectual Proper...
General Principles of Intellectual Property: Concepts of Intellectual  Proper...General Principles of Intellectual Property: Concepts of Intellectual  Proper...
General Principles of Intellectual Property: Concepts of Intellectual Proper...
 
Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)
 
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxPython Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docx
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
 

Find dimension and a basis of the following vector spacesSoluti.pdf

  • 1. Find dimension and a basis of the following vector spaces: Solution So all polynomials with roots:-1,1 and 2 So multiples of polynomial: f(x)=(x+1)(x-1)(x-2) which is polynomial of degree 3 But degree must be less than 6 So basis is :B={f(x),xf(x),x^2f(x),x^3f(x)} So 4 vectors in basis HEnce dimension =4