MATH 107 • Tüm Sınavlar • Linear Algebra

Augmented Matrix - Row Reduction 1

Augmented Matrix - Row Reduction 2

Existence and Uniqueness of Solution

Free Variables

Exam-like Questions 1

Exam-like Questions 2

Exam-like Questions 3

Exam-like Questions 4

Exam like Question 5

Vector Properties

Linear Combination 1

Linear Combination 2

Formal Definition of Linear Combination

Span of Vectors 1

Span of Vectors 2

Exam-like Question 6

Exam-like Question 7

Exam-like Question 8

Exam-like Question 9

Exam-like Question 10

Matrix Equations and Augmented Matrix

Solutions of Homogeneous Linear Systems

Solutions of Non-Homogeneous Linear Systems

Exam-like Question 11

Exam-like Question 12

Exam-like Question 13

Exam-like Question 14

Theorem for Matrix Equations

Exam-like Questions 15

Exam-like Questions 16

Exam-like Questions 17

Linear Independent Sets

Exam-like Questions 18

Exam-like Questions 19

Exam like Question 20

Exam-like Questions 21

Exam-like Questions 22

Exam-like Questions 23

Fundamental Matrix Operations

Inverse of a Matrix 1

Inverse of a Matrix 2

Exam-like Question 24

Exam-like Question 25

Exam-like Question 26

Exam-like Question 27

Exam-like Question 28

Exam-like Question 29

Exam-like Question 30

Elementary Matrix

Inverse of Elementary Matrix

Exam-like Question 31

Exam-like Question 32

Exam-like Question 33

Linear Transformations 1

Linear Transformation 2

Exam like Question 34

Exam like Question 35

Matrix of a Linear Transformation

Exam like Question 36

Inverse of Linear Transformation 1

Inverse of Linear Transformation 2

Exam like Question 37

Systems of Equations

Systems of Equations 2

Systems of Equations

Systems of Equations

Existence and Uniqueness

Existence and Uniqueness

Existence and Uniqueness

Linear Independence

Linear Independence 2

Linear Independence 3

Trivial & Nontrivial Solution (Spring 2018)

Span of Vectors 1

Span of Vectors 2

Span of Vectors 3

Span of Vectors

Span of Vectors

Span of Vectors 5

Nonhomogeneous Systems 1

Nonhomogeneous Systems 2

Nonhomogeneous Systems

Nonhomogeneous Systems 4

Invertibility 1

Invertibility

Invertibility

Solving equations by Inverse

Linear Transformation 1

Linear Transformation 2

Linear Transformation 3

Matrix of Linear Transformation 1

Matrix of Linear Transformation 2

Inverse of Linear Transformation 1

Inverse of Linear Transformation 2

Inverse of Linear Transformation 3

Composite of Linear Transformation 1

Reflection of a Transformation 1

Reflection of a Transformation 2

Reflection of a Transformation

Theory Problem

Theory Problem

Theory Problem

Theory Problem

Theory Problem

Theory Problem

Vector Spaces and Subspaces

Matrix Subspace 1

Matrix Subspace 2

Matrix Subspace 3

Matrix Subspace 4

Matrix Subspace 5

Matrix Subspace 6

Polynomial Subspace 1

Polynomial Subspace 2

Polynomial Subspace 3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Matrix Product

Linear Independence

Inverse Matrix

Linear Transformation and Linear Independence

Vector Subspaces

Vector Subspaces

Vector Subspaces

Systems of Linear Equations

Linear Transformations

Inverse Matrix

Linear Independence

Theory Problem: Invertibility

Theory Problem: Spanning Set

Systems of Linear Equations

Linear Independence

Span of Vectors

Matrix of Linear Transformation

Linear Transformation: One to One & Onto

True-False Theory Problems

Proof Problem

Proof Problem 1

Proof Problem 2

Proof Problem 3

Proof Problem 4

Proof Problem 5

Proof Problem 6

Proof Problem 7

Proof Problem 8

Proof Problem 9

Proof Problem 10

Proof Problem 11

Determinant & Cofactor Expansion

Determinants of Bigger Matrices

Properties of Determinant

Properties of Determinant 2

Applications of Determinants - Area & Volume

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Exam-like Question 5

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 Polynomial Subspaces

Basis for Matrix Subspaces

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Exam-like Question 5

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

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

Isomorphism 1

Isomorphism 2

Isomorphism 3

Exam like Question 1

Exam like Question 2

Properties of Determinants 1

Properties of Determinants 2

Properties of Determinants 3

Properties of Determinants 4

Vector Spaces and Subspaces

Matrix Subspace 1

Matrix Subspace 2

Matrix Subspace 3

Matrix Subspace 4

Matrix Subspace 5

Matrix Subspace 6

Polynomial Subspace 1

Polynomial Subspace 2

Polynomial Subspace 3

Column, Null and Row Spaces 1

Column, Null and Row Spaces 2

Column, Null and Row Spaces 3

Rank, Column and Null Spaces

Rank, Column and Null Spaces 2

Rank, Column and Null Spaces 3

Rank, Column and Null Spaces 4

Column, Null and Row Spaces 5

Basis for Subspaces 1

Basis for Subspaces 2

Basis for Subspaces 3

Basis for Subspaces 4

Basis for Subspaces 5

Basis for Subspaces 6

Linear Transformation & Determinant

Basis for Kernel and Range 1

Basis for Kernel and Range 2

Basis for Kernel and Range 3

Basis for Kernel and Range 4

Basis for Kernel and Range 5

Basis for Kernel and Range 6

Polynomial Basis 1

Polynomial Basis 2

Polynomial Basis 3

Polynomial Basis 4

Polynomial Basis 5

Subspaces or not ?

Matrix of Linear Transformation

Spanning Set - Kernel and Range

Isomorphism

True-False Theory Problems

Theory Problem: Linear Transformation

Proof Problem 1

Proof Problem 2

Proof Problem 3

Proof Problem 4

Proof Problem 5

Proof Problem 6

Proof Problem 7

Proof Problem 8

Proof Problem 9

Proof with Determinant I

Proof with Determinant II

Theory Problem 1-5

Theory Problem 5-10

Theory Problem 10-15

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

Transformation Matrix Relative to Basis 1

Transformation Matrix Relative to Basis 2

Transformation Matrix Relative to Basis 3

Key concepts for orthogonality

Orthogonal Complement

Orthagonal Complement 2

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam like Question 4

Orthogonal Sets and Basis

Advantage of an Orthogonal Basis

Orthonormal Sets and Basis

Orthogonal Matrix

Orthogonal Projection 1

Orthogonal Projection 2

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

The Gram-Schmidt Process 1

The Gram-Schmidt Process 2

Exam like Question 1

Exam like Question 2

Diagonalization

Diagonalization

Diagonalization

Diagonalization

Diagonalization

Transformations & Eigenvalues 1

Transformations & Eigenvalues 2

Transformations & Eigenvalues 3

Transformations & Eigenvalues 4

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

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

Harvard Type Question 1

Harvard Type Question 2

Harvard Type Question 3

Harvard Type Question 4

Harvard Type Question 5

Harvard Type Question 6

Harvard Type Question 7

Harvard Type Question 8

Harvard Type Question 9

Diagonalization

Orthogonal Complements

Gram-Schmidt Process

Gram-Schmidt Process

Gram-Schmidt Process

Linear Transformations & Eigenvalues

Linear Transformations & Eigenvalues

Linear Transformation & Change of Basis

Linear Transformation & Change of Basis

Linear Transformation & Change of Basis