COM 105 • Midterm + Final • Linear Algebra
Eğitmenler
Dorukhan Özcan
Co-Founder & CEO
Unicourse şirketinin kurucu ortağıyım. 2016 senesinde Galatasaray Lisesinden mezun oldum. Geçtiğimiz dört sene içerisinde 2000 saatten fazla ders anlattım. Anlattığım dersler sırasıyla; Calculus, Çok değişkenli Calculus, Lineer Cebir, Differansiyel Denklemler, Uygulamalı İstatistik ve Stokastik Modelleme dersleridir. Doping Hafıza şirketinde 2017 - 2022 seneleri arasında CEO danışmanlığı yaptım. Koç Üniversitesi Endüstri Mühendisliği ve Ekonomi çift anadal programını tam burslu olarak, 3.96/4.00 not ortalamasıyla bitirdim. Kadıköy Modalıyım.
Tolga Temiz
Eğitmen
2016 senesinde başladığım Koç Üniversitesi Matematik bölümünden 2020 senesinde fakülte üçüncüsü olarak mezun oldum. Lisans ve yüksek lisans eğitimlerim boyunca çeşitli derslerde asistanlık yaptım. 2021'de Koç Üniversitesi'nde Matematik yüksek lisansına başladım ve 2023 yılında mezun oldum. Şimdi Michigan State Üniversitesi'nde doktora yapıyorum. Topoloji alanıyla ilgilenmekteyim.
Kerem Başol
Eğitmen
2019 senesinde Koç Üniversitesi Matematik bölümüne başladım. Geçtiğimiz senelerde Calculus ve Linear Algebra derslerinde Tutor ve Teaching Assistant pozisyonlarında görev aldım. Halen Koç Üniversitesi Matematik ve Bilgisayar Mühendisliği çift anadal programını 4.00/4.00 ortalamayla fakülte birincisi olarak sürdürüyorum. Trigonometrik fonksiyonların elips üzerinde nasıl tanımlanabileceğini merak etmemle başlayan Matematik tutkumu aktarmak için Unicourse Matematik Zümresine katıldım.
Unicourse Garantisi
Bu dersi alma kararını senin için kolaylaştıralım. Eğer memnun kalmazsan 30 gün içinde bize ulaş, 3'ten fazla içerik tamamlamadıysan iade alabilirsin. Koşullar
Konular
Inner Product Space
1 konu anlatımı · 3 soru
Inner Product Space
Exam like Question 1
Exam like Question 2
Exam like Question 3
Systems of Linear Equations
4 konu anlatımı · 7 soru
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
Problem 1
Problem 2
Problem 3
Matrix Operations
1 konu anlatımı · 5 soru
Fundamental Matrix Operations
Problem 1
Problem 2
Problem 4
Problem 6
Problem 7
Inverse of a Matrix
2 konu anlatımı · 4 soru
Inverse of a Matrix 1
Inverse of a Matrix 2
Problem 1
Problem 2
Problem 3
Problem 4
Matrix Equations (AX = B Formu)
3 konu anlatımı
Product of a Matrix and a Vector
Matrix Equation
Solving AX = B with Inverse
Linear Combination & Span of Vectors
4 konu anlatımı · 2 soru
Vectors and Linear Combination
Linear Combination 2
Linear Combination - Span of vectors
Span of Vectors 2
Exam-like Question 1
Exam-like Question 5
Matrix Equations
3 konu anlatımı · 3 soru
Matrix Equations and Augmented Matrix
Solutions of Homogeneous Linear Systems
Solutions of Non-Homogeneous Linear Systems
Exam-like Question 1
Exam-like Question 2
Exam-like Question 5
Fundamental Theorem for Matrix Equations
1 konu anlatımı · 2 soru
Theorem for Matrix Equations
Exam-like Questions 1
Exam-like Questions 3
Linear Independence
1 konu anlatımı · 3 soru
Linear Independent Sets
Exam-like Questions 4
Exam-like Questions 5
Exam-like Questions 6
Matrix Operations and Inverse of a Matrix
3 konu anlatımı · 5 soru
Fundamental Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
Exam-like Question 25
Exam-like Question 26
Exam-like Question 28
Exam-like Question 29
Exam-like Question 32
Elementary Matrices
2 konu anlatımı · 2 soru
Elementary Matrix
Inverse of Elementary Matrix
Exam-like Question 34
Exam-like Question 36
Linear Transformation
4 konu anlatımı · 1 soru
Linear Transformations 1
Linear Transformation 2
Exam like Question 1
Matrix of a Linear Transformation
Linearity of Transformations
Vector Spaces and Subspaces
2 konu anlatımı · 5 soru
Vector Spaces and Subspaces 1
Vector Spaces and Subspaces 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Matrix Spaces and Matrix Subspaces
1 konu anlatımı
Matrix Spaces & Matrix Subspaces
Subspaces and Polynomials
1 konu anlatımı · 2 soru
Polynomial Subspaces
Exam-like Question 15
Exam-like Question 16
Null Space & Column Space & Row Space
1 konu anlatımı · 1 soru
Null Space & Column Space & Row Space
Exam-like Question 17
Basis for Subspaces
1 konu anlatımı · 3 soru
Bases for Col A & Row A & Null A
Exam-like Question 18
Exam-like Question 19
Exam-like Question 20
Basis for Subspaces 2
3 konu anlatımı · 5 soru
Basis for Vector Subspaces
Basis for Polynomial Subspaces
Basis for Matrix Subspaces
Exam-like Question 21
Exam-like Question 22
Exam-like Question 23
Exam-like Question 24
Exam-like Question 25
Linear Transformation: Basis for Kernel and Range
7 konu anlatımı
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
9 konu anlatımı · 8 soru
Coordinate Systems: Introduction
Exam-like Question 26
Exam-like Question 27
Coordinate Systems: Polynomials
Exam-like Question 28
Exam like Question 29
Exam-like Question 30
Exam like Question 31
Exam-like Question 32
Exam like Question 33
Coordinate Systems-1
Coordinate Systems-2
Coordinate Systems-3
Coordinate Systems-4
Coordinate Systems-5
Coordinate Systems-6
Coordinate Systems-7
Change of Basis
1 konu anlatımı · 5 soru
Change of Basis
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam-like Question 4
Exam like Question 5
Rank of a Matrix
2 konu anlatımı
Rank of a Matrix 1
Rank of a Matrix 2
Isomorphism
3 konu anlatımı · 2 soru
Isomorphism 1
Konu - 2
Konu - 3
Isomorphism 1
Isomorphism 2
Change of Basis on Linear Transformations
1 konu anlatımı · 12 soru
Change of Basis and Linear Transformations
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
Determinants
2 konu anlatımı · 6 soru
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 38
Properties of Determinants
2 konu anlatımı · 3 soru
Properties of Determinant
Properties of Determinant 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Cramer's Rule
1 konu anlatımı · 4 soru
Cramer's Rule 1
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Eigenvalues and Eigenvectors
10 konu anlatımı
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
Complex Eigenvalues
Complex Eigenvalues-2
Similarity and Diagonalization-1
Similarity and Diagonalization-2
Linear Transformation & Eigenvectors
8 konu anlatımı
Linear Transformations & Eigenvectors 1
Linear Transformations & Eigenvectors 2
Linear Transformations & Eigenvectors 3
Linear Transformations & Eigenvectors 4
Eigenvalue & Eigenvectors & Diagonalization 1
Eigenvalue & Eigenvectors & Diagonalization 2
Eigenvalue & Eigenvectors & Diagonalization 3
Eigenvalue & Eigenvectors & Diagonalization 4
Orthogonality
3 konu anlatımı · 5 soru
Key concepts for orthogonality
Exam-like Question 1
Orthogonality and Orthogonal Complement
Orthagonal Complement 2
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Orthogonal Sets
4 konu anlatımı · 1 soru
Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Exam-like Question 6
Orthonormal Sets and Basis
Orthogonal Matrix
Orthogonal Projection
2 konu anlatımı · 4 soru
Orthogonal Projection 1
Exam-like Question 7
Exam-like Question 8
Orthogonal Projection 2
Exam-like Question 9
Exam-like Question 10
The Gram-Schmidt Process
2 konu anlatımı
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Past Exam Questions 1
35 soru
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
Past Exam Questions 2
30 soru
Existence and Uniqueness
Existence and Uniqueness
Null & Column & Row Spaces, Rank
Null & Column & Row Spaces, Rank
Null & Column & Row Spaces, Rank
Null & Column & Row Spaces
Theory: Null & Column & Row Spaces, Rank
Kernel and Image of Transformations
Kernel and Image of Transformations
Kernel and Image of Transformations
Kernel and Image of Transformations
Kernel and Image of Transformations
Finding the Matrix of Transformations
Finding the Matrix of Transformations
Finding the Matrix of Transformations
Finding the Matrix of Transformations
Change of Basis
Diagonalization
Diagonalization
Diagonalization
Transformations & Eigenvectors
Transformations & Eigenvalues
Transformations & Eigenvectors
True-False Problems 1-4
True-False Problems 5-8
True-False Problems 9-12
Bonus
Bonus
Bonus
Bonus
Past Exam Questions 3
35 soru
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
Past Exam Questions 4
53 soru
Systems of Equations
Spring 2022 Exam: Systems of Equations 2
Spring 2021 Exam: Systems of Equations
Fall 2022 Exam: Systems of Equations
Spring 2022 Exam: Existence and Uniqueness
Fall 2021 Exam: Existence and Uniqueness
Spring 2021 Exam: Existence and Uniqueness
Fall 2020 Exam: Linear Independence
Linear Independence 2
Linear Independence 3
Trivial & Nontrivial Solution (Spring 2018)
Spring 2018: Span of Vectors 1
Span of Vectors 2 (Spring 2021)
Span of Vectors 3
Fall 2021 Exam: Span of Vectors
Fall 2022 Exam: Span of Vectors
Span of Vectors 5 (Spring 2022)
Nonhomogeneous Systems 1
Nonhomogeneous Systems 2
Fall 2021 Exam: Nonhomogeneous Systems
Nonhomogeneous Systems 4 (Spring 2021)
Invertibility 1
Fall 2020 Exam: Invertibility
Fall 2022 Exam: Invertibility
Solving equations by Inverse
Linear Transformation 1 (Summer 2017)
Linear Transformation 2 (Fall 2020)
Linear Transformation 3
Matrix of Linear Transformation 1
Matrix of Linear Transformation 2
Inverse of Linear Transformation 1 (Spring 2017)
Inverse of Linear Transformation 2
Inverse of Linear Transformation 3
Composite of Linear Transformation 1
Reflection of a Transformation 1
Spring 2017: Reflection of a Transformation 2
Spring 2021 Exam: Reflection of a Transformation
Fall 2022 Exam: Theory Problem
Fall 2022 Exam: Theory Problem
Fall 2022 Exam: Theory Problem
Theory Problem
Spring 2023 Exam: Theory Problem
Spring 2023 Exam: 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