T 1) (core) Is the following linear transformation injective? Surjective? (Justify both with full entences). T(x, y, z) = (3x - 2y, 4y - 8z, x + 10z)

Use concepts from below and provide explanation.

Chapter 1 Linear Equations in Linear Algebra

1-1 Systems of Linear Equations 

1-2 Row Reduction and Echelon Forms

1-3 Vector Equations 

1-4 The Matrix Equation Ax = b 

1-5 Solution Sets of Linear Systems

1-6 Applications of Linear Systems

1-7 Linear Independence 

1-8 Introduction to Linear Transformations

1-9 The Matrix of a Linear Transformation 

Chapter 2 Matrix Algebra

2-1 Matrix Operations 

2-2 The Inverse of a Matrix 

2-3 Characterizations of Invertible Matrices

2-4 Partitioned Matrices 

2-5 Matrix Factorizations 

2-6 The Leontief Input-Output Model 

2-7 Applications to Computer Graphics

Chapter 3 Determinants

3-1 Introduction to Determinants 172

3-2 Properties of Determinants 179

3-3 Cramer's Rule, Volume, and Linear Transformations

Chapter 4 Vector Spaces

4-1 Vector Spaces and Subspaces

4-2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations 

4-3 Linearly Independent Sets; Bases

4-4 Coordinate Systems

4-5 The Dimension of a vector space

4-6 Change of Basis

4-7 Digital Signal Processing

4-8 Applications to Difference Equations

Chapter 5 Eigenvalues and Eigenvectors

5-1 Eigenvalues and Eigenvectors

5-2 The Characteristic Equation

5-3 Diaganolization

5-4 Eigenvectors. And Linear Transformation

5-5 Complex Eigenvalues

5-6 Discrete Dynamical Systems