SlideShare uma empresa Scribd logo
1 de 1
Baixar para ler offline
Linear Algebra please show all work. Question 1 (5 points). Consider the following statement
and proof: Let V be a vector space over F. Then for alpha, beta E F and x E V, we have (alpha
x)beta = alpha (x beta). Proof. We have and this shows the equality. Using the definition sheet,
justify each equality in the proof: (1) Equality follows from (2) Equality follows from (3)
Equality follows from (4) Equality follows from (5) Equality follows from
Solution
jhj

Mais conteúdo relacionado

Mais de airflyluggage

like many entreneurs, Tony Smith started Sonic as a sole proprietors.pdf
like many entreneurs, Tony Smith started Sonic as a sole proprietors.pdflike many entreneurs, Tony Smith started Sonic as a sole proprietors.pdf
like many entreneurs, Tony Smith started Sonic as a sole proprietors.pdfairflyluggage
 
Like a sole proprietorship statement of owners equity, the stateme.pdf
Like a sole proprietorship statement of owners equity, the stateme.pdfLike a sole proprietorship statement of owners equity, the stateme.pdf
Like a sole proprietorship statement of owners equity, the stateme.pdfairflyluggage
 
Lewotontin wrote a critical review of The Social Organization of Sex.pdf
Lewotontin wrote a critical review of The Social Organization of Sex.pdfLewotontin wrote a critical review of The Social Organization of Sex.pdf
Lewotontin wrote a critical review of The Social Organization of Sex.pdfairflyluggage
 
Let Z_{n} denote the sample mean for a random sample of size n from.pdf
Let Z_{n} denote the sample mean for a random sample of size n from.pdfLet Z_{n} denote the sample mean for a random sample of size n from.pdf
Let Z_{n} denote the sample mean for a random sample of size n from.pdfairflyluggage
 
LetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdf
LetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdfLetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdf
LetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdfairflyluggage
 
Lets say you frequently drink wine thats been rated highly by Ro.pdf
Lets say you frequently drink wine thats been rated highly by Ro.pdfLets say you frequently drink wine thats been rated highly by Ro.pdf
Lets say you frequently drink wine thats been rated highly by Ro.pdfairflyluggage
 
Let X1,X2, . . . be a sequence of independent identically distribute.pdf
Let X1,X2, . . . be a sequence of independent identically distribute.pdfLet X1,X2, . . . be a sequence of independent identically distribute.pdf
Let X1,X2, . . . be a sequence of independent identically distribute.pdfairflyluggage
 
Let X1,X2,X3 and X4 be independent random variables. Assume that X2.pdf
Let X1,X2,X3 and X4 be independent random variables.  Assume that X2.pdfLet X1,X2,X3 and X4 be independent random variables.  Assume that X2.pdf
Let X1,X2,X3 and X4 be independent random variables. Assume that X2.pdfairflyluggage
 
Let X1,X2,X3....X25 be a random sample from a population with mean o.pdf
Let X1,X2,X3....X25 be a random sample from a population with mean o.pdfLet X1,X2,X3....X25 be a random sample from a population with mean o.pdf
Let X1,X2,X3....X25 be a random sample from a population with mean o.pdfairflyluggage
 
Let Y1 and Y2 be independent and uniformly distributed over the inte.pdf
Let Y1 and Y2 be independent and uniformly distributed over the inte.pdfLet Y1 and Y2 be independent and uniformly distributed over the inte.pdf
Let Y1 and Y2 be independent and uniformly distributed over the inte.pdfairflyluggage
 
Let Y1 be the number of success in n = 10 independent Bernoulli tria.pdf
Let Y1 be the number of success in n = 10 independent Bernoulli tria.pdfLet Y1 be the number of success in n = 10 independent Bernoulli tria.pdf
Let Y1 be the number of success in n = 10 independent Bernoulli tria.pdfairflyluggage
 
Let Y have an exponential distribution with mean . Prove that W.pdf
Let Y have an exponential distribution with mean .     Prove that W.pdfLet Y have an exponential distribution with mean .     Prove that W.pdf
Let Y have an exponential distribution with mean . Prove that W.pdfairflyluggage
 
Let Y be a continuous random variable and define m as the median of .pdf
Let Y be a continuous random variable and define m as the median of .pdfLet Y be a continuous random variable and define m as the median of .pdf
Let Y be a continuous random variable and define m as the median of .pdfairflyluggage
 
Let X1,...,Xn represent a random sample from the discrete distributi.pdf
Let X1,...,Xn represent a random sample from the discrete distributi.pdfLet X1,...,Xn represent a random sample from the discrete distributi.pdf
Let X1,...,Xn represent a random sample from the discrete distributi.pdfairflyluggage
 
Let X1,...,X5 be Independent continuous random variables having comm.pdf
Let X1,...,X5 be Independent continuous random variables having comm.pdfLet X1,...,X5 be Independent continuous random variables having comm.pdf
Let X1,...,X5 be Independent continuous random variables having comm.pdfairflyluggage
 
Let X1 and X2 have a trinomial distribution. Differentiate the momen.pdf
Let X1 and X2 have a trinomial distribution. Differentiate the momen.pdfLet X1 and X2 have a trinomial distribution. Differentiate the momen.pdf
Let X1 and X2 have a trinomial distribution. Differentiate the momen.pdfairflyluggage
 

Mais de airflyluggage (16)

like many entreneurs, Tony Smith started Sonic as a sole proprietors.pdf
like many entreneurs, Tony Smith started Sonic as a sole proprietors.pdflike many entreneurs, Tony Smith started Sonic as a sole proprietors.pdf
like many entreneurs, Tony Smith started Sonic as a sole proprietors.pdf
 
Like a sole proprietorship statement of owners equity, the stateme.pdf
Like a sole proprietorship statement of owners equity, the stateme.pdfLike a sole proprietorship statement of owners equity, the stateme.pdf
Like a sole proprietorship statement of owners equity, the stateme.pdf
 
Lewotontin wrote a critical review of The Social Organization of Sex.pdf
Lewotontin wrote a critical review of The Social Organization of Sex.pdfLewotontin wrote a critical review of The Social Organization of Sex.pdf
Lewotontin wrote a critical review of The Social Organization of Sex.pdf
 
Let Z_{n} denote the sample mean for a random sample of size n from.pdf
Let Z_{n} denote the sample mean for a random sample of size n from.pdfLet Z_{n} denote the sample mean for a random sample of size n from.pdf
Let Z_{n} denote the sample mean for a random sample of size n from.pdf
 
LetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdf
LetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdfLetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdf
LetX_1, X_2, . . . , X_nbe i.i.d. from distributionF 1. IfFis t.pdf
 
Lets say you frequently drink wine thats been rated highly by Ro.pdf
Lets say you frequently drink wine thats been rated highly by Ro.pdfLets say you frequently drink wine thats been rated highly by Ro.pdf
Lets say you frequently drink wine thats been rated highly by Ro.pdf
 
Let X1,X2, . . . be a sequence of independent identically distribute.pdf
Let X1,X2, . . . be a sequence of independent identically distribute.pdfLet X1,X2, . . . be a sequence of independent identically distribute.pdf
Let X1,X2, . . . be a sequence of independent identically distribute.pdf
 
Let X1,X2,X3 and X4 be independent random variables. Assume that X2.pdf
Let X1,X2,X3 and X4 be independent random variables.  Assume that X2.pdfLet X1,X2,X3 and X4 be independent random variables.  Assume that X2.pdf
Let X1,X2,X3 and X4 be independent random variables. Assume that X2.pdf
 
Let X1,X2,X3....X25 be a random sample from a population with mean o.pdf
Let X1,X2,X3....X25 be a random sample from a population with mean o.pdfLet X1,X2,X3....X25 be a random sample from a population with mean o.pdf
Let X1,X2,X3....X25 be a random sample from a population with mean o.pdf
 
Let Y1 and Y2 be independent and uniformly distributed over the inte.pdf
Let Y1 and Y2 be independent and uniformly distributed over the inte.pdfLet Y1 and Y2 be independent and uniformly distributed over the inte.pdf
Let Y1 and Y2 be independent and uniformly distributed over the inte.pdf
 
Let Y1 be the number of success in n = 10 independent Bernoulli tria.pdf
Let Y1 be the number of success in n = 10 independent Bernoulli tria.pdfLet Y1 be the number of success in n = 10 independent Bernoulli tria.pdf
Let Y1 be the number of success in n = 10 independent Bernoulli tria.pdf
 
Let Y have an exponential distribution with mean . Prove that W.pdf
Let Y have an exponential distribution with mean .     Prove that W.pdfLet Y have an exponential distribution with mean .     Prove that W.pdf
Let Y have an exponential distribution with mean . Prove that W.pdf
 
Let Y be a continuous random variable and define m as the median of .pdf
Let Y be a continuous random variable and define m as the median of .pdfLet Y be a continuous random variable and define m as the median of .pdf
Let Y be a continuous random variable and define m as the median of .pdf
 
Let X1,...,Xn represent a random sample from the discrete distributi.pdf
Let X1,...,Xn represent a random sample from the discrete distributi.pdfLet X1,...,Xn represent a random sample from the discrete distributi.pdf
Let X1,...,Xn represent a random sample from the discrete distributi.pdf
 
Let X1,...,X5 be Independent continuous random variables having comm.pdf
Let X1,...,X5 be Independent continuous random variables having comm.pdfLet X1,...,X5 be Independent continuous random variables having comm.pdf
Let X1,...,X5 be Independent continuous random variables having comm.pdf
 
Let X1 and X2 have a trinomial distribution. Differentiate the momen.pdf
Let X1 and X2 have a trinomial distribution. Differentiate the momen.pdfLet X1 and X2 have a trinomial distribution. Differentiate the momen.pdf
Let X1 and X2 have a trinomial distribution. Differentiate the momen.pdf
 

Último

Student login on Anyboli platform.helpin
Student login on Anyboli platform.helpinStudent login on Anyboli platform.helpin
Student login on Anyboli platform.helpinRaunakKeshri1
 
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionMastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionSafetyChain Software
 
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdfBASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdfSoniaTolstoy
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)eniolaolutunde
 
Measures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SDMeasures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SDThiyagu K
 
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...EduSkills OECD
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactPECB
 
CARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptxCARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptxGaneshChakor2
 
Disha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdfDisha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdfchloefrazer622
 
Separation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and ActinidesSeparation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and ActinidesFatimaKhan178732
 
Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104misteraugie
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationnomboosow
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformChameera Dedduwage
 
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...Sapna Thakur
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdfQucHHunhnh
 
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Sapana Sha
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingTechSoup
 

Último (20)

Student login on Anyboli platform.helpin
Student login on Anyboli platform.helpinStudent login on Anyboli platform.helpin
Student login on Anyboli platform.helpin
 
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionMastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory Inspection
 
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdfBASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)
 
Measures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SDMeasures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SD
 
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
 
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
 
CARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptxCARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptx
 
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptxINDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
 
Disha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdfDisha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdf
 
Separation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and ActinidesSeparation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and Actinides
 
Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communication
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
 
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
 
Mattingly "AI & Prompt Design: The Basics of Prompt Design"
Mattingly "AI & Prompt Design: The Basics of Prompt Design"Mattingly "AI & Prompt Design: The Basics of Prompt Design"
Mattingly "AI & Prompt Design: The Basics of Prompt Design"
 
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy Consulting
 

Linear Algebra please show all work. Question 1 (5 points). Consider.pdf

  • 1. Linear Algebra please show all work. Question 1 (5 points). Consider the following statement and proof: Let V be a vector space over F. Then for alpha, beta E F and x E V, we have (alpha x)beta = alpha (x beta). Proof. We have and this shows the equality. Using the definition sheet, justify each equality in the proof: (1) Equality follows from (2) Equality follows from (3) Equality follows from (4) Equality follows from (5) Equality follows from Solution jhj