MATH 221 • Final: Part I • 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

Linear Independent Sets

Linear Independence of Matrices

Linear Independence & Theory

Exam-like Questions 1

Exam-like Questions 2

Exam-like Question 3

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

Null Space & Column Space & Row Space

Bases for Col A & Row A & Null A

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Basis for Vector Subspaces

Basis for Matrix Subspaces

Basis for Polynomial Subspaces

Exam-like Question 4

Exam-like Question 5

Exam-like Question 6

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

Change of Basis : Vector Spaces

Change of Basis : Polynomials

Change of Basis: Matrices

Linear Transformations 1

Linear Transformation 2

Linearity of Transformations

Matrix of a Linear Transformation

Exam like Question 1

Exam-like Question 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

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

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Column,Null and Row Spaces

Basis and Linear Dependence

Linear Transformations

Linear Transformations & Change of Basis

Linear Transformations & Change of Basis

Linear Transformations & Change of Basis

Theory Problem

Proof Problem 1

Proof Problem 2

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