MATH 225 • Midterm • Linear Algebra and Differential Equations
Konular
Systems of Linear Equations
Augmented Matrix - Row Operations 1
Augmented Matrix - Row Operations 2
Existence and Uniqueness of Solution
Free Variables
Exam-like Questions 1
Exam-like Questions 2
Exam like Question 3
Matrix Operations and Inverse
Fundamental Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
Exam-like Question 1
Exam-like Question 2
Exam like Question 3
Matrix Equations
Matrix Equation
Solving AX = B with Inverse
Exam like Question 1
Exam-like Question 2
Exam like Question 3
Elementary Matrices
Elementary Matrix
Inverse of Elementary Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Determinants
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant
Properties of Determinant 2
Cramer's Rule
Adjoint Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Vectors: Linear Combination and Span
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 Independence
Linear Independent Sets
Linear Independence of Matrices
Special Theorem for Matrix Equation
Exam-like Questions 1
Exam-like Questions 2
Exam-like Question 3
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Polynomial Subspaces
Matrix Spaces & Matrix 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
Basis for Subspaces: Row and Column Spaces
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Basis for Polynomial Subspaces 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Orthogonality
Key concepts for orthogonality
Orthogonal Complement
Orthagonal Complement 2
Orthogonal Sets and Basis
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Eigenvalues and Eigenvectors
Eigenvalues & Eigenvectors : 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Algebraic and Geometric Multiplicities
Eigenspace of Matrices
Complex Eigenvalues
Complex Eigenvalues 2
Diagonalization of Matrices
Diagonalization 1
Diagonalization 2
Exam like Question 1
Exam like Question 2
Sample Midterm Part I
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3 (Fall 2021)
Matrix Operations (Spring 2022)
Elementary Matrices 1
Elementary Matrices 2 (Fall 2021)
Determinant and Invertibility
Properties of Determinants 1
Properties of Determinants 2 (Fall 2020)
Sample Midterm Part II
Subspace or not 1
Subspace or not 2
Subspaces or not 3 (Fall 2022)
Subspaces or not 4 (Fall 2022)
Subspaces or not 5
Basis for Subspaces 1
Basis for Subspaces 2 (Spring 2023)
Basis for Subspaces 2
Basis for Subspaces 3
Basis for Subspaces 4
Basis for Subspaces 5 (Spring 2022)
Polynomials Basis 1
Polynomials Basis 2
Polynomials Basis 3
Polynomials Basis 4 (Fall 2020)
Polynomials Basis 5
Null & Column & Row Spaces
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3 (Fall 2020)
Null & Column & Row Spaces 4
Null & Column & Row Spaces 5 (Fall 2021)
Diagonalization 1
Diagonalization 2
Orthogonal Complement 1
Orthogonal Complement 2
Orthogonal Complement 3
Orthogonal Complement 4
Orthogonal Complement (Fall 2021)
Orthogonal Complement (Spring 2023)
Orthogonal Complement (Fall 2020)
Theory Problem 1
Theory Problem 2
Theory Problem 3 (Spring 2022)
Theory Problem 4 (Spring 2022)
(NEW) Spring 2024 Exam
Existence and Uniqueness of Solution
Determinants
Elementary Matrices
Determinant and Invertibility
Basis and Subspaces
Basis and Subspaces
(NEW) Fall 2024 Exam
Systems of Linear Equations
Row Reduction
Determinant
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Orthogonality
Orthogonality
Eğitmenler
Dorukhan Özcan
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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.
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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.
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