H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/...
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Transcript of H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/...
![Page 1: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/1.jpg)
H.Melikian/1200 1
Linear Algebra II
Dr .Hayk Melikyan/ Departmen of Mathematics and CS/ [email protected]
Linear Transformations and Matrices (Sec 2.7)
Composition and Invertibility of Linear Transformations (Sec 2.8
![Page 2: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/2.jpg)
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Functions and Mappings
![Page 3: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/3.jpg)
H.Melikian/1200 3
Transformations Induced by Matrices
![Page 4: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/4.jpg)
H.Melikian/1200 4
Properties of Matrix Transformation
![Page 5: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/5.jpg)
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Linear Transformations
![Page 6: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/6.jpg)
H.Melikian/1200 6
Properties of Linear Transformations
![Page 7: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/7.jpg)
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Composition and Invertibility of Linear Transformations (Sec 2.8)
![Page 8: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/8.jpg)
H.Melikian/1200 8
Properties of onto Maps
![Page 9: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/9.jpg)
H.Melikian/1200 9
One-to-one maps and Null Space of Transformation
![Page 10: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/10.jpg)
H.Melikian/1200 10
Example.
Determine whether the given linear transformation is one-to-one, onto or both
![Page 11: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/11.jpg)
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Composition of Maps
![Page 12: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/12.jpg)
H.Melikian/1200 12
Composition of Matrix transformations
![Page 13: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.](https://reader030.fdocuments.in/reader030/viewer/2022032803/56649e2a5503460f94b18a11/html5/thumbnails/13.jpg)
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Invertibility of Linear Transformation