MATH 211 • Midterm I • Linear Algebra
“Konuların en temel mantığı olmasa da sınav için gerekli olan kısımları ifadeleri tamamıyla açık bir şekilde öğrendim.”
Mehmet Emin Yıldırım
Elektrik-Elektronik Mühendisliği
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.
Paketi Tamamla
🎓 Özyeğin Üniversitesi öğrencilerinin %92'si tüm paketi alarak çalışıyor.
Konular
Ch 1.1-2: Systems of Linear Equations
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
Ch 1.3: Vector Equations
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
Ch 1.4-5: Matrix Equations & Solution Sets of Linear Systems
Matrix Equations and Augmented Matrix
Solutions of Homogeneous Linear Systems
Solutions of Non-Homogeneous Linear Systems
Theorem for Matrix Equations
Exam-like Question 11
Exam-like Question 12
Exam-like Question 13
Exam-like Question 14
Exam-like Questions 15
Exam-like Questions 16
Exam-like Questions 17
Ch 1.7: Linear Independence
Linear Independent Sets
Exam-like Questions 18
Exam-like Questions 19
Exam-like Questions 20
Exam-like Questions 21
Exam-like Questions 22
Ch 2.1-3: Matrix Operations and Inverse of a Matrix
Fundamental Matrix Operations
Characterizations of Invertible Matrices
Finding the Inverse of a Matrix
Solving AX = B with Inverse
Exam like Question 23
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
Midterm Practice Problems Part I
Systems of Equations 1
Systems of Equations 2
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence and Uniqueness 4
Trivial & Nontrivial Solution
Linear Independence 1
Linear Independence 2
Span of Vectors 1
Span of Vectors 2
Invertibility 1
Invertibility 2
Invertibility 3
Solving Systems with Inverse 1
Solving Systems with Inverse 2
Nonhomogeneous Systems 1
Nonhomogeneous Systems 2
Ch 1.8: Linear Transformation
Linear Transformations 1
Linear Transformation 2
Exam like Question 33
Exam like Question 34
Ch1.9: The Matrix of a Linear Transformation
Matrix of a Linear Transformation
Exam like Question 35
Ch 3.1-2: Determinant and Properties
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant I
Properties of Determinant II
Exam like Question 36
Exam like Question 37
Exam like Question 38
Exam like Question 39
Exam like Question 40
Exam like Question 41
Exam like Question 42
Midterm Practice Problems Part II
Linear Transformation 1
Linear Transformation 2
Determinants 1
Properties of Determinants 1
Properties of Determinants 2
Properties of Determinants 3
(NEW) Fall 2023 Exam Problems
Span of Vectors & Linear Independence
Invertibility of a Matrix
Determinant & Co-factor Expansion
Linear Transformations
(NEW) Spring 2024 Exam Problems
Existence and Uniqueness
Invertibility of a Matrix
Span of Vectors
Matrix Operations
Linear Transformations
(NEW) Fall 2024 Exam Problems
Vector Equations
The Matrix of a Linear Transformation
Inverse of a Matrix
Determinant
Unicourse Special Review Problems
Linear Independence
Linear Independence
Existence and Uniqueness
Solving Systems with Inverse
Solving Systems with Inverse
Matrix of Linear Transformation
Matrix of Linear Transformation
Determinants
Determinants & Invertibility
Determinants & Linear Independence
Properties of Determinants
Challenging Problem: Span of Vectors
Değerlendirmeler
Yardımcı oldu
Konuların en temel mantığı olmasa da sınav için gerekli olan kısımları ifadeleri tamamıyla açık bir şekilde öğrendim.
Sıkça Sorulan Sorular
Örneğin, Koç Üniversitesi - MATH 101 (Calculus) veya başka bir okulun benzer dersi olsun, paketlerimiz tam da o derse göre tasarlanır. Böylece nokta atışı çalışır, zaman kazanırsın.
Sınava özel videolar —konu anlatımları, çıkmış sorular ve çözümleri, özet notlar—içerir. Sınavda sıkça çıkan soruları hedefler. Eğitmenlerimiz, üniversitenin akademik takvimini takip ederek paketleri sürekli günceller. Böylece, gereksiz detaylarla vakit kaybetmeden başarını artırmaya odaklanabilirsin.
Ders İçeriği
Ch 1.1-2: Systems of Linear Equations
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
Ch 1.3: Vector Equations
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
Ch 1.4-5: Matrix Equations & Solution Sets of Linear Systems
Matrix Equations and Augmented Matrix
Solutions of Homogeneous Linear Systems
Solutions of Non-Homogeneous Linear Systems
Theorem for Matrix Equations
Exam-like Question 11
Exam-like Question 12
Exam-like Question 13
Exam-like Question 14
Exam-like Questions 15
Exam-like Questions 16
Exam-like Questions 17
Ch 1.7: Linear Independence
Linear Independent Sets
Exam-like Questions 18
Exam-like Questions 19
Exam-like Questions 20
Exam-like Questions 21
Exam-like Questions 22
Ch 2.1-3: Matrix Operations and Inverse of a Matrix
Fundamental Matrix Operations
Characterizations of Invertible Matrices
Finding the Inverse of a Matrix
Solving AX = B with Inverse
Exam like Question 23
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
Midterm Practice Problems Part I
Systems of Equations 1
Systems of Equations 2
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence and Uniqueness 4
Trivial & Nontrivial Solution
Linear Independence 1
Linear Independence 2
Span of Vectors 1
Span of Vectors 2
Invertibility 1
Invertibility 2
Invertibility 3
Solving Systems with Inverse 1
Solving Systems with Inverse 2
Nonhomogeneous Systems 1
Nonhomogeneous Systems 2
Ch 1.8: Linear Transformation
Linear Transformations 1
Linear Transformation 2
Exam like Question 33
Exam like Question 34
Ch1.9: The Matrix of a Linear Transformation
Matrix of a Linear Transformation
Exam like Question 35
Ch 3.1-2: Determinant and Properties
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant I
Properties of Determinant II
Exam like Question 36
Exam like Question 37
Exam like Question 38
Exam like Question 39
Exam like Question 40
Exam like Question 41
Exam like Question 42
Midterm Practice Problems Part II
Linear Transformation 1
Linear Transformation 2
Determinants 1
Properties of Determinants 1
Properties of Determinants 2
Properties of Determinants 3
(NEW) Fall 2023 Exam Problems
Span of Vectors & Linear Independence
Invertibility of a Matrix
Determinant & Co-factor Expansion
Linear Transformations
(NEW) Spring 2024 Exam Problems
Existence and Uniqueness
Invertibility of a Matrix
Span of Vectors
Matrix Operations
Linear Transformations
(NEW) Fall 2024 Exam Problems
Vector Equations
The Matrix of a Linear Transformation
Inverse of a Matrix
Determinant
Unicourse Special Review Problems
Linear Independence
Linear Independence
Existence and Uniqueness
Solving Systems with Inverse
Solving Systems with Inverse
Matrix of Linear Transformation
Matrix of Linear Transformation
Determinants
Determinants & Invertibility
Determinants & Linear Independence
Properties of Determinants
Challenging Problem: Span of Vectors