let be z a fixed angle . if x belong to R2, let L(x)be the element.pdf

A

amitagrawal1410

Seguir

•0 recomendaciones•2 vistas

let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru the angle z . assume L:R-R is linear . let u1=e1, u2=e2. then u1,u2 form a basisfor R2 . find a formula for L(x) j hint: first determine v1=L(u1) and v2=L(u2)k let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru the angle z . assume L:R-R is linear . let u1=e1, u2=e2. then u1,u2 form a basisfor R2 . find a formula for L(x) j hint: first determine v1=L(u1) and v2=L(u2)k Solution First consider the 2x2 matrix that rotates vectors in R^2 by an angle of z: \\( A = \\left( \\begin{array}{cc} cos(z) & -sin(z) \\\\ sin(z) & cos(z) \\end{array} \ ight) \\) Let \\( x = [x_1, x_2]^T = x_1e_1 + x_2e_2 \\). Then \\( Ax = \\left( \\begin{array} { c } cos(z) x_1 - sin(z) x_2 \\\\ sin(z) x_1 + cos(z) x_2 \\end{array} \ ight) \\) Therefore we define linear transformation L: R^2 --> R^2 by \\( L(x) = (cos(z) x_1 - sin(z) x_2, sin(z) x_1 + cos(z) x_2 ) \\) where \\( x = (x_1, x_2) \\)..

let be z a fixed angle . if x belong to R2, let L(x)be the element.pdf

•0 recomendaciones•2 vistas

A

amitagrawal1410

Seguir

let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru the angle z . assume L:R-R is linear . let u1=e1, u2=e2. then u1,u2 form a basisfor R2 . find a formula for L(x) j hint: first determine v1=L(u1) and v2=L(u2)k let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru the angle z . assume L:R-R is linear . let u1=e1, u2=e2. then u1,u2 form a basisfor R2 . find a formula for L(x) j hint: first determine v1=L(u1) and v2=L(u2)k Solution First consider the 2x2 matrix that rotates vectors in R^2 by an angle of z: \\( A = \\left( \\begin{array}{cc} cos(z) & -sin(z) \\\\ sin(z) & cos(z) \\end{array} \ ight) \\) Let \\( x = [x_1, x_2]^T = x_1e_1 + x_2e_2 \\). Then \\( Ax = \\left( \\begin{array} { c } cos(z) x_1 - sin(z) x_2 \\\\ sin(z) x_1 + cos(z) x_2 \\end{array} \ ight) \\) Therefore we define linear transformation L: R^2 --> R^2 by \\( L(x) = (cos(z) x_1 - sin(z) x_2, sin(z) x_1 + cos(z) x_2 ) \\) where \\( x = (x_1, x_2) \\)..

let be z a fixed angle . if x belong to R2, let L(x)be the element.pdf

1 de 2

let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru
the angle z .
assume L:R-R is linear .
let u1=e1, u2=e2.
then u1,u2 form a basisfor R2 .
find a formula for L(x) j
hint: first determine v1=L(u1) and v2=L(u2)k
let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru
the angle z .
assume L:R-R is linear .
let u1=e1, u2=e2.
then u1,u2 form a basisfor R2 .
find a formula for L(x) j
hint: first determine v1=L(u1) and v2=L(u2)k
Solution
First consider the 2x2 matrix that rotates vectors in R^2 by an angle of z:
( A = left( begin{array}{cc} cos(z) & -sin(z) sin(z) & cos(z) end{array} ight) )
Let ( x = [x_1, x_2]^T = x_1e_1 + x_2e_2 ). Then
( Ax = left( begin{array} { c } cos(z) x_1 - sin(z) x_2 sin(z) x_1 + cos(z) x_2
end{array} ight) )
Therefore we define linear transformation L: R^2 --> R^2 by
( L(x) = (cos(z) x_1 - sin(z) x_2, sin(z) x_1 + cos(z) x_2 ) )

where ( x = (x_1, x_2) ).

Recomendados

OrthogonalFunctionsPaper por

OrthogonalFunctionsPaper

OrthogonalFunctionsPaper

OrthogonalFunctionsPaperTyler Otto

522 vistas•19 diapositivas

Algebraic techniques in combinatorics por

Algebraic techniques in combinatorics

Algebraic techniques in combinatorics

Algebraic techniques in combinatoricsVui Lên Bạn Nhé

322 vistas•6 diapositivas

A transference result of Lp continuity from the Jacobi Riesz transform to the... por

A transference result of Lp continuity from the Jacobi Riesz transform to the...

A transference result of Lp continuity from the Jacobi Riesz transform to the...

A transference result of Lp continuity from the Jacobi Riesz transform to the...Wilfredo Urbina

336 vistas•33 diapositivas

ThesisAspen DeVries

146 vistas•34 diapositivas

eigenvalueAsyraf Ghani

1.3K vistas•20 diapositivas

Sol75eli priyatna laidan

104 vistas•5 diapositivas

Más contenido relacionado

Similar a let be z a fixed angle . if x belong to R2, let L(x)be the element.pdf

Circles (XYZ).pdf por

Circles (XYZ).pdf

Circles (XYZ).pdf

Circles (XYZ).pdfSTUDY INNOVATIONS

26 vistas•12 diapositivas

Lecture_note2.pdf por

Lecture_note2.pdf

Lecture_note2.pdf

Lecture_note2.pdfEssaAlMadhagi

56 vistas•37 diapositivas

Parabola-01-Theory por

Parabola-01-Theory

Parabola-01-Theory

Parabola-01-TheorySTUDY INNOVATIONS

16 vistas•21 diapositivas

Lecture5Atner Yegorov

447 vistas•6 diapositivas

On the lambert w function por

On the lambert w function

On the lambert w function

On the lambert w functionTrungKienVu3

425 vistas•32 diapositivas

Summer Proj. por

Summer Proj.Patrick Hough

286 vistas•36 diapositivas

Similar a let be z a fixed angle . if x belong to R2, let L(x)be the element.pdf(20)

Circles (XYZ).pdf por STUDY INNOVATIONS

Circles (XYZ).pdf

Circles (XYZ).pdf

Circles (XYZ).pdf

STUDY INNOVATIONS•26 vistas

Lecture_note2.pdf por EssaAlMadhagi

Lecture_note2.pdf

Lecture_note2.pdf

Lecture_note2.pdf

EssaAlMadhagi•56 vistas

Parabola-01-Theory por STUDY INNOVATIONS

Parabola-01-Theory

Parabola-01-Theory

Parabola-01-Theory

STUDY INNOVATIONS•16 vistas

Lecture5 por Atner Yegorov

Lecture5

Lecture5

Lecture5

Atner Yegorov•447 vistas

On the lambert w function por TrungKienVu3

On the lambert w function

On the lambert w function

On the lambert w function

TrungKienVu3•425 vistas

Summer Proj. por Patrick Hough

Summer Proj.

Summer Proj.

Summer Proj.

Patrick Hough•286 vistas

Please answer all questions Suppose we have two independent.pdf por aglowcollection

Please answer all questions Suppose we have two independent.pdf

Please answer all questions Suppose we have two independent.pdf

Please answer all questions Suppose we have two independent.pdf

aglowcollection•2 vistas

Matrix calculus por Sungbin Lim

Matrix calculus

Matrix calculus

Matrix calculus

Sungbin Lim•10.4K vistas

Linear Algebra por Maths Tutoring

Linear Algebra

Linear Algebra

Linear Algebra

Maths Tutoring•36 vistas

4 ftc and signed areas x por math266

4 ftc and signed areas x

4 ftc and signed areas x

4 ftc and signed areas x

math266•430 vistas

6.6 analyzing graphs of quadratic functions por Jessica Garcia

6.6 analyzing graphs of quadratic functions

6.6 analyzing graphs of quadratic functions

6.6 analyzing graphs of quadratic functions

Jessica Garcia•26.4K vistas

003 circle por physics101

003 circle

003 circle

003 circle

physics101•6.8K vistas

Ch07 6 por Rendy Robert

Ch07 6

Ch07 6

Ch07 6

Rendy Robert•525 vistas

1a)Find parametric equations of the line of the intersection of the pl (2).docx por lcarolyn

1a)Find parametric equations of the line of the intersection of the pl (2).docx

1a)Find parametric equations of the line of the intersection of the pl (2).docx

1a)Find parametric equations of the line of the intersection of the pl (2).docx

lcarolyn•2 vistas

2.6ellipses x por math260

2.6ellipses x

2.6ellipses x

2.6ellipses x

math260•597 vistas

Surfaces quadric por Führer-Ex Sami

Surfaces quadric

Surfaces quadric

Surfaces quadric

Führer-Ex Sami•878 vistas

Cse41 por Krishna Gali

Cse41

Cse41

Cse41

Krishna Gali•467 vistas

Parabola 091102134314-phpapp01 por A.

Parabola 091102134314-phpapp01

Parabola 091102134314-phpapp01

Parabola 091102134314-phpapp01

A. •2.2K vistas

Eigen values and eigenvectors por Amit Singh

Eigen values and eigenvectors

Eigen values and eigenvectors

Eigen values and eigenvectors

Amit Singh•4.9K vistas

Parabola (TN).pdf por STUDY INNOVATIONS

Parabola (TN).pdf

Parabola (TN).pdf

Parabola (TN).pdf

STUDY INNOVATIONS•37 vistas

Más de amitagrawal1410

Let f, g R -- R be functions such that f is continuous at x_0 and.pdf por

Let f, g R -- R be functions such that f is continuous at x_0 and.pdf

Let f, g R -- R be functions such that f is continuous at x_0 and.pdf

Let f, g R -- R be functions such that f is continuous at x_0 and.pdfamitagrawal1410

2 vistas•1 diapositiva

Let f, g R -- R be functions. Prove, using the sequence definitio.pdf por

Let f, g R -- R be functions. Prove, using the sequence definitio.pdf

Let f, g R -- R be functions. Prove, using the sequence definitio.pdf

Let f, g R -- R be functions. Prove, using the sequence definitio.pdfamitagrawal1410

2 vistas•1 diapositiva

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdf por

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdf

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdf

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdfamitagrawal1410

4 vistas•1 diapositiva

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdf por

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdf

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdf

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdfamitagrawal1410

2 vistas•1 diapositiva

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdf por

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdf

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdf

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdfamitagrawal1410

3 vistas•1 diapositiva

Let f and g befunctions between A and B. Prove that f =g iff domf.pdf por

Let f and g befunctions between A and B. Prove that f =g iff domf.pdf

Let f and g befunctions between A and B. Prove that f =g iff domf.pdf

Let f and g befunctions between A and B. Prove that f =g iff domf.pdfamitagrawal1410

2 vistas•1 diapositiva

Más de amitagrawal1410(20)

Let f, g R -- R be functions such that f is continuous at x_0 and.pdf por amitagrawal1410

Let f, g R -- R be functions such that f is continuous at x_0 and.pdf

Let f, g R -- R be functions such that f is continuous at x_0 and.pdf

Let f, g R -- R be functions such that f is continuous at x_0 and.pdf

amitagrawal1410•2 vistas

Let f, g R -- R be functions. Prove, using the sequence definitio.pdf por amitagrawal1410

Let f, g R -- R be functions. Prove, using the sequence definitio.pdf

Let f, g R -- R be functions. Prove, using the sequence definitio.pdf

Let f, g R -- R be functions. Prove, using the sequence definitio.pdf

amitagrawal1410•2 vistas

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdf por amitagrawal1410

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdf

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdf

Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k.pdf

amitagrawal1410•4 vistas

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdf por amitagrawal1410

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdf

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdf

Let f(x) = 0 if x is irrational and f(p SolutionFor every rati.pdf

amitagrawal1410•2 vistas

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdf por amitagrawal1410

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdf

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdf

Let f Z--Z be defined by f(n)= {n+2, if n is even, 2n, if n is odd.pdf

amitagrawal1410•3 vistas

Let f and g befunctions between A and B. Prove that f =g iff domf.pdf por amitagrawal1410

Let f and g befunctions between A and B. Prove that f =g iff domf.pdf

Let f and g befunctions between A and B. Prove that f =g iff domf.pdf

Let f and g befunctions between A and B. Prove that f =g iff domf.pdf

amitagrawal1410•2 vistas

Let F be a field with exactly q elements. Show that a^q = a for all .pdf por amitagrawal1410

Let F be a field with exactly q elements. Show that a^q = a for all .pdf

Let F be a field with exactly q elements. Show that a^q = a for all .pdf

Let F be a field with exactly q elements. Show that a^q = a for all .pdf

amitagrawal1410•2 vistas

Let F be a field. Prove that the only ideals of F are F and {0}S.pdf por amitagrawal1410

Let F be a field. Prove that the only ideals of F are F and {0}S.pdf

Let F be a field. Prove that the only ideals of F are F and {0}S.pdf

Let F be a field. Prove that the only ideals of F are F and {0}S.pdf

amitagrawal1410•5 vistas

Let f and g be functions from R to R determine if this statement is .pdf por amitagrawal1410

Let f and g be functions from R to R determine if this statement is .pdf

Let f and g be functions from R to R determine if this statement is .pdf

Let f and g be functions from R to R determine if this statement is .pdf

amitagrawal1410•2 vistas

Let F (n) denote the n-th term of the Fibonacci Sequence. Prove usin.pdf por amitagrawal1410

Let F (n) denote the n-th term of the Fibonacci Sequence. Prove usin.pdf

Let F (n) denote the n-th term of the Fibonacci Sequence. Prove usin.pdf

Let F (n) denote the n-th term of the Fibonacci Sequence. Prove usin.pdf

amitagrawal1410•2 vistas

Let f and g be functions. Either prove or give a counterexample to t.pdf por amitagrawal1410

Let f and g be functions. Either prove or give a counterexample to t.pdf

Let f and g be functions. Either prove or give a counterexample to t.pdf

Let f and g be functions. Either prove or give a counterexample to t.pdf

amitagrawal1410•2 vistas

Let f (0,1)-- R be an arbitrary function with the properties i).pdf por amitagrawal1410

Let f (0,1)-- R be an arbitrary function with the properties i).pdf

Let f (0,1)-- R be an arbitrary function with the properties i).pdf

Let f (0,1)-- R be an arbitrary function with the properties i).pdf

amitagrawal1410•2 vistas

Let E and F are mutually exclusive and P(E) = 0.2 and P(F) = 0.5. F.pdf por amitagrawal1410

Let E and F are mutually exclusive and P(E) = 0.2 and P(F) = 0.5. F.pdf

Let E and F are mutually exclusive and P(E) = 0.2 and P(F) = 0.5. F.pdf

Let E and F are mutually exclusive and P(E) = 0.2 and P(F) = 0.5. F.pdf

amitagrawal1410•2 vistas

Let D = (V,A) a directed graph, let R a closed directed walk in D. D.pdf por amitagrawal1410

Let D = (V,A) a directed graph, let R a closed directed walk in D. D.pdf

Let D = (V,A) a directed graph, let R a closed directed walk in D. D.pdf

Let D = (V,A) a directed graph, let R a closed directed walk in D. D.pdf

amitagrawal1410•3 vistas

Let B be a partition of the nonempty set A. For x and ybelonging to(.pdf por amitagrawal1410

Let B be a partition of the nonempty set A. For x and ybelonging to(.pdf

Let B be a partition of the nonempty set A. For x and ybelonging to(.pdf

Let B be a partition of the nonempty set A. For x and ybelonging to(.pdf

amitagrawal1410•2 vistas

let B={(2,1,1,-1),(1,-3,1,0),(-1,3,10,11),(1,0,-1,1)}in R4, show tha.pdf por amitagrawal1410

let B={(2,1,1,-1),(1,-3,1,0),(-1,3,10,11),(1,0,-1,1)}in R4, show tha.pdf

let B={(2,1,1,-1),(1,-3,1,0),(-1,3,10,11),(1,0,-1,1)}in R4, show tha.pdf

let B={(2,1,1,-1),(1,-3,1,0),(-1,3,10,11),(1,0,-1,1)}in R4, show tha.pdf

amitagrawal1410•2 vistas

Let A=4 -1 25 x 7x -1 3For what values o.pdf por amitagrawal1410

Let A=4 -1 25 x 7x -1 3For what values o.pdf

Let A=4 -1 25 x 7x -1 3For what values o.pdf

Let A=4 -1 25 x 7x -1 3For what values o.pdf

amitagrawal1410•2 vistas

Let A1, A2, A3 be events with probabilities .04, .16, and .5, respec.pdf por amitagrawal1410

Let A1, A2, A3 be events with probabilities .04, .16, and .5, respec.pdf

Let A1, A2, A3 be events with probabilities .04, .16, and .5, respec.pdf

Let A1, A2, A3 be events with probabilities .04, .16, and .5, respec.pdf

amitagrawal1410•2 vistas

Let a,b,c, and d be intergers. Prove that if a I b and c I d , then .pdf por amitagrawal1410

Let a,b,c, and d be intergers. Prove that if a I b and c I d , then .pdf

Let a,b,c, and d be intergers. Prove that if a I b and c I d , then .pdf

Let a,b,c, and d be intergers. Prove that if a I b and c I d , then .pdf

amitagrawal1410•2 vistas

Let a,b be in a ring A. Suppose that neither a nor b is 0 and that n.pdf por amitagrawal1410

Let a,b be in a ring A. Suppose that neither a nor b is 0 and that n.pdf

Let a,b be in a ring A. Suppose that neither a nor b is 0 and that n.pdf

Let a,b be in a ring A. Suppose that neither a nor b is 0 and that n.pdf

amitagrawal1410•2 vistas

Último

Class 10 English notes 23-24.pptx por

Class 10 English notes 23-24.pptx

Class 10 English notes 23-24.pptx

Class 10 English notes 23-24.pptxTARIQ KHAN

107 vistas•53 diapositivas

discussion post.pdf por

discussion post.pdf

discussion post.pdf

discussion post.pdfjessemercerail

120 vistas•1 diapositiva

Psychology KS5 por

Psychology KS5WestHatch

77 vistas•5 diapositivas

Universe revised.pdf por

Universe revised.pdf

Universe revised.pdf

Universe revised.pdfDrHafizKosar

112 vistas•26 diapositivas

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively por

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks EffectivelyPECB

545 vistas•18 diapositivas

Education and Diversity.pptx por

Education and Diversity.pptx

Education and Diversity.pptx

Education and Diversity.pptxDrHafizKosar

118 vistas•16 diapositivas

Último(20)

Class 10 English notes 23-24.pptx por TARIQ KHAN

Class 10 English notes 23-24.pptx

Class 10 English notes 23-24.pptx

Class 10 English notes 23-24.pptx

TARIQ KHAN•107 vistas

discussion post.pdf por jessemercerail

discussion post.pdf

discussion post.pdf

discussion post.pdf

jessemercerail•120 vistas

Psychology KS5 por WestHatch

Psychology KS5

Psychology KS5

Psychology KS5

WestHatch•77 vistas

Universe revised.pdf por DrHafizKosar

Universe revised.pdf

Universe revised.pdf

Universe revised.pdf

DrHafizKosar•112 vistas

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively por PECB

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively

ISO/IEC 27001 and ISO/IEC 27005: Managing AI Risks Effectively

PECB •545 vistas

Education and Diversity.pptx por DrHafizKosar

Education and Diversity.pptx

Education and Diversity.pptx

Education and Diversity.pptx

DrHafizKosar•118 vistas

Compare the flora and fauna of Kerala and Chhattisgarh ( Charttabulation) por AnshulDewangan3

Compare the flora and fauna of Kerala and Chhattisgarh ( Charttabulation)

Compare the flora and fauna of Kerala and Chhattisgarh ( Charttabulation)

Compare the flora and fauna of Kerala and Chhattisgarh ( Charttabulation)

AnshulDewangan3•316 vistas

Class 10 English lesson plans por TARIQ KHAN

Class 10 English lesson plans

Class 10 English lesson plans

Class 10 English lesson plans

TARIQ KHAN•257 vistas

Student Voice por Pooky Knightsmith

Student Voice

Student Voice

Student Voice

Pooky Knightsmith•164 vistas

Gopal Chakraborty Memorial Quiz 2.0 Prelims.pptx por Debapriya Chakraborty

Gopal Chakraborty Memorial Quiz 2.0 Prelims.pptx

Gopal Chakraborty Memorial Quiz 2.0 Prelims.pptx

Gopal Chakraborty Memorial Quiz 2.0 Prelims.pptx

Debapriya Chakraborty•598 vistas

BYSC infopack.pdf por Fundacja Rozwoju Społeczeństwa Przedsiębiorczego

BYSC infopack.pdf

BYSC infopack.pdf

BYSC infopack.pdf

Fundacja Rozwoju Społeczeństwa Przedsiębiorczego•173 vistas

STERILITY TEST.pptx por Anupkumar Sharma

STERILITY TEST.pptx

STERILITY TEST.pptx

STERILITY TEST.pptx

Anupkumar Sharma•125 vistas

Women from Hackney’s History: Stoke Newington by Sue Doe por History of Stoke Newington

Women from Hackney’s History: Stoke Newington by Sue Doe

Women from Hackney’s History: Stoke Newington by Sue Doe

Women from Hackney’s History: Stoke Newington by Sue Doe

History of Stoke Newington•141 vistas

Structure and Functions of Cell.pdf por Nithya Murugan

Structure and Functions of Cell.pdf

Structure and Functions of Cell.pdf

Structure and Functions of Cell.pdf

Nithya Murugan•368 vistas

UWP OA Week Presentation (1).pptx por Jisc

UWP OA Week Presentation (1).pptx

UWP OA Week Presentation (1).pptx

UWP OA Week Presentation (1).pptx

Jisc•74 vistas

ANATOMY AND PHYSIOLOGY UNIT 1 { PART-1} por DR .PALLAVI PATHANIA

ANATOMY AND PHYSIOLOGY UNIT 1 { PART-1}

ANATOMY AND PHYSIOLOGY UNIT 1 { PART-1}

ANATOMY AND PHYSIOLOGY UNIT 1 { PART-1}

DR .PALLAVI PATHANIA•240 vistas

Psychology KS4 por WestHatch

Psychology KS4

Psychology KS4

Psychology KS4

WestHatch•68 vistas

American Psychological Association 7th Edition.pptx por SamiullahAfridi4

American Psychological Association 7th Edition.pptx

American Psychological Association 7th Edition.pptx

American Psychological Association 7th Edition.pptx

SamiullahAfridi4•82 vistas

Drama KS5 Breakdown por WestHatch

Drama KS5 Breakdown

Drama KS5 Breakdown

Drama KS5 Breakdown

WestHatch•71 vistas

EIT-Digital_Spohrer_AI_Intro 20231128 v1.pptx por ISSIP

EIT-Digital_Spohrer_AI_Intro 20231128 v1.pptx

EIT-Digital_Spohrer_AI_Intro 20231128 v1.pptx

EIT-Digital_Spohrer_AI_Intro 20231128 v1.pptx

ISSIP•317 vistas

let be z a fixed angle . if x belong to R2, let L(x)be the element.pdf

1. let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru the angle z . assume L:R-R is linear . let u1=e1, u2=e2. then u1,u2 form a basisfor R2 . find a formula for L(x) j hint: first determine v1=L(u1) and v2=L(u2)k let be z a fixed angle . if x belong to R2, let L(x)be the element of R2 obtained by rotating x thru the angle z . assume L:R-R is linear . let u1=e1, u2=e2. then u1,u2 form a basisfor R2 . find a formula for L(x) j hint: first determine v1=L(u1) and v2=L(u2)k Solution First consider the 2x2 matrix that rotates vectors in R^2 by an angle of z: ( A = left( begin{array}{cc} cos(z) & -sin(z) sin(z) & cos(z) end{array} ight) ) Let ( x = [x_1, x_2]^T = x_1e_1 + x_2e_2 ). Then ( Ax = left( begin{array} { c } cos(z) x_1 - sin(z) x_2 sin(z) x_1 + cos(z) x_2 end{array} ight) ) Therefore we define linear transformation L: R^2 --> R^2 by ( L(x) = (cos(z) x_1 - sin(z) x_2, sin(z) x_1 + cos(z) x_2 ) )

2. where ( x = (x_1, x_2) ).