IND 2119550 • Final • Linear Algebra

Vector Properties

Linear Combination 1

Linear Combination 2

Formal Definition of Linear Combination

Span of Vectors 1

Span of Vectors 2

Solutions of Homogeneous Linear Systems

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Solutions of Non-Homogeneous Linear Systems

Exam-like Question 1

Exam-like Question 2

Exam like Question 3

Exam like Question 4

Linear Independent Sets

Linear Independence of Matrices

Special Theorem for Matrix Equation

Exam-like Questions 1

Exam-like Questions 2

Exam-like Question 3

Exam-like Question 4

Vector Spaces and Subspaces

Matrix Spaces & Matrix Subspaces

Polynomial Subspaces

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

Null Space & Column Space & Row Space

Bases for Col A & Row A & Null A

Exam like Question

Basis for Vector Subspaces

Basis for Matrix Subspaces

Basis for Polynomial Subspaces

Basis for Polynomial Subspaces 2

Coordinate Systems : Introduction

Coordinate Systems : Polynomials

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam like Question 4

Exam like Question 5

Coordinate Systems : Matrices 1

Coordinate Systems : Matrices 2

Coordinate Systems : Matrices 3

Coordinate Systems : Matrices 4

Change of Basis : Vector Spaces

Change of Basis : Polynomials

Change of Basis: Matrices

Linear Transformations 1

Linear Transformation 2

Matrix of a Linear Transformation

Linearity of Transformations

Inverse of Linear Transformation 1

Inverse of Linear Transformation 2

Basis for Kernel and Range of a Transformation

Basis for Kernel and Range of a Transformation 2

Basis for Kernel and Range of a Transformation 3

Linear Independence of Matrices

Basis for Kernel and Range of a Transformation 4

Basis for Kernel and Range of a Transformation 5

Basis for Kernel and Range of a Transformation 6

Transformation Matrix Relative to Basis 1

Transformation Matrix Relative to Basis 2

Transformation Matrix Relative to Basis 3

Exam like Question 1

Exam like Question 2

Eigenvalues & Eigenvectors : 3 Vital Steps

Eigenvalues & Eigenvectors: A Special Tip

A Matrix with Irrational Eigenvalues

Algebraic and Geometric Multiplicities 1

Algebraic and Geometric Multiplicities-2

Eigenspace of Matrices

Diagonalization 1

Diagonalization 2

Exam like Question

Span of Vectors

Span of Vectors

Span of Vectors

Span of Vectors

Span of Vectors

Linear Independence

Linear Independence

Linear Independence

Linear Independence

Null & Column & Row Spaces 1

Null & Column & Row Spaces 2

Null & Column & Row Spaces 3

Null & Column & Row Spaces 4

Null & Column & Row Spaces 5

Column,Null and Row Spaces 1

Column,Null and Row Spaces 2

Column,Null and Row Spaces 3

Basis for Subspaces (Vectors)

Basis for Subspaces (Vectors)

Basis for Subspaces (Vectors)

Basis for Subspaces (Vectors)

Basis for Subspaces (Matrices)

Basis for Subspaces (Matrices)

Basis for Subspaces (Matrices)

Basis for Subspaces (Matrices)

Basis for Subspaces (Matrices)

Basis for Subspaces (Matrices)

Basis for Subspaces (Matrices)

Basis for Subspaces (Matrices)

Basis for Subspaces (Polynomials)

Basis for Subspaces (Polynomials)

Basis for Subspaces (Polynomials)

Basis for Subspaces (Polynomials)

Spanning Sets (Vectors)

Spanning Sets (Vectors)

Spanning Sets (Vectors)

Spanning Sets (Vectors)

Spanning Sets (Polynomials)

Spanning Sets (Polynomials)

Spanning Sets (Polynomials)

Spanning Sets (Matrices)

Linear Independence of Polynomials

Linear Transformations

Linear Transformations

Linear Transformations

Linear Transformations

Linear Transformation

Linear Transformation

Inverse of Linear Transformation

Inverse of Linear Transformation

Composite of Linear Transformation

Reflection of a Transformation

Reflection of a Transformation

Reflection of a Transformation

Basis for Kernel and Range

Basis for Kernel and Range

Basis for Kernel and Range

Basis for Kernel and Range

Transformations & Change of Basis 1

Transformations & Change of Basis 2

Transformations & Change of Basis 3

Transformations & Change of Basis 4

Transformations & Change of Basis 5

Transformations & Change of Basis 6

Transformations & Change of Basis 7

Transformations & Change of Basis 8

Transformations & Change of Basis 9

Eigenvalues

Diagonalization

Diagonalization

Diagonalization

Diagonalization

Diagonalization

Eigenvalues and Eigenvectors

Eigenvalues and Eigenvectors