h.melikian/12001 linear algebra ii dr.hayk melikyan/ departmen of mathematics and cs/...

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H.Melikian/1200 1

Linear Algebra II

Dr .Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu

Linear Transformations and Matrices (Sec 2.7)

Composition and Invertibility of Linear Transformations (Sec 2.8

H.Melikian/1200 2

Functions and Mappings

H.Melikian/1200 3

Transformations Induced by Matrices

H.Melikian/1200 4

Properties of Matrix Transformation

H.Melikian/1200 5

Linear Transformations

H.Melikian/1200 6

Properties of Linear Transformations

H.Melikian/1200 7

Composition and Invertibility of Linear Transformations (Sec 2.8)

H.Melikian/1200 8

Properties of onto Maps

H.Melikian/1200 9

One-to-one maps and Null Space of Transformation

H.Melikian/1200 10

Example.

Determine whether the given linear transformation is one-to-one, onto or both

H.Melikian/1200 11

Composition of Maps

H.Melikian/1200 12

Composition of Matrix transformations

H.Melikian/1200 13

Invertibility of Linear Transformation

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