MATH 225 • Midterm • Linear Algebra and Differential Equations
Sınava 10 gün kaldı.
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.
Sınava 10 gün kaldı.
Paketi Tamamla
🎓 Bilkent Üniversitesinde öğrencilerin %92'si tüm paketi alarak çalışıyor.
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
General Review Problems
Existence and Uniqueness
Elementary Matrices
Determinant and Invertibility
Properties of Determinants
Subspace or not 1
Subspace or not 2
Subspaces or not 3
Basis for Subspaces 1
Basis for Subspaces 2
Basis for Subspaces 3
Basis for Subspaces 4
Polynomials Basis 1
Polynomials Basis 2
Polynomials Basis 3
Polynomials Basis 4
Null & Column & Row Spaces
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3
Orthogonal Complement 1
Orthogonal Complement 2
Orthogonal Complement 3
Orthogonal Complement 4
Theory Problem 1
Theory Problem 2
Past Exam Problems
Fall 2021 Exam: Existence and Uniqueness
Fall 2020 Exam: Existence and Uniqueness
Fall 2021 Exam: Elementary Matrices
Spring 2022 Exam: Inverse & Elementary Matrices
Fall 2020 Exam: Properties of Determinants
Fall 2022 Exam: Subspaces or not ?
Fall 2022 Exam: Subspaces or not ?
Spring 2023 Exam: Basis for Subspaces
Spring 2022 Exam: Basis for Subspaces
Fall 2020 Exam: Polynomials Basis
Fall 2020 Exam: Null & Column & Row Spaces
Fall 2020: Rank of a Matrix
Fall 2021 Exam: Null & Column & Row Spaces
Fall 2021 Exam: Orthogonal Complement
Spring 2023 Exam: Orthogonal Complement
Fall 2020 Exam: Orthogonal Complement
Fall 2020 Exam: Theory Problem I
Fall 2020 Exam: Theory Problem II
Fall 2020 Exam: Theory Problem III
Fall 2020 Exam: Theory Problem IV
Spring 2022 Exam: Theory Problem I
Spring 2022 Exam: Theory Problem II
Spring 2024 Exam
Existence and Uniqueness of Solution
Determinants
Elementary Matrices
Determinant and Invertibility
Basis and Subspaces
Basis and Subspaces
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
Fall 2024 Midterm Prep Set
Null Space & Column Space
Matrix Operations & Invertibility
Determinant
Theory Problem
Vector Subspaces
Vector Subspaces
Dimension of Subspaces
Inner Product Space
Orthogonal Complement & Inner Product Space
Değerlendirmeler
Ders İçeriği
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
General Review Problems
Existence and Uniqueness
Elementary Matrices
Determinant and Invertibility
Properties of Determinants
Subspace or not 1
Subspace or not 2
Subspaces or not 3
Basis for Subspaces 1
Basis for Subspaces 2
Basis for Subspaces 3
Basis for Subspaces 4
Polynomials Basis 1
Polynomials Basis 2
Polynomials Basis 3
Polynomials Basis 4
Null & Column & Row Spaces
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3
Orthogonal Complement 1
Orthogonal Complement 2
Orthogonal Complement 3
Orthogonal Complement 4
Theory Problem 1
Theory Problem 2
Past Exam Problems
Fall 2021 Exam: Existence and Uniqueness
Fall 2020 Exam: Existence and Uniqueness
Fall 2021 Exam: Elementary Matrices
Spring 2022 Exam: Inverse & Elementary Matrices
Fall 2020 Exam: Properties of Determinants
Fall 2022 Exam: Subspaces or not ?
Fall 2022 Exam: Subspaces or not ?
Spring 2023 Exam: Basis for Subspaces
Spring 2022 Exam: Basis for Subspaces
Fall 2020 Exam: Polynomials Basis
Fall 2020 Exam: Null & Column & Row Spaces
Fall 2020: Rank of a Matrix
Fall 2021 Exam: Null & Column & Row Spaces
Fall 2021 Exam: Orthogonal Complement
Spring 2023 Exam: Orthogonal Complement
Fall 2020 Exam: Orthogonal Complement
Fall 2020 Exam: Theory Problem I
Fall 2020 Exam: Theory Problem II
Fall 2020 Exam: Theory Problem III
Fall 2020 Exam: Theory Problem IV
Spring 2022 Exam: Theory Problem I
Spring 2022 Exam: Theory Problem II
Spring 2024 Exam
Existence and Uniqueness of Solution
Determinants
Elementary Matrices
Determinant and Invertibility
Basis and Subspaces
Basis and Subspaces
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
Fall 2024 Midterm Prep Set
Null Space & Column Space
Matrix Operations & Invertibility
Determinant
Theory Problem
Vector Subspaces
Vector Subspaces
Dimension of Subspaces
Inner Product Space
Orthogonal Complement & Inner Product Space
Sınava 10 gün kaldı.
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.