MATH 211 • Midterm II + Final • 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 Üniversitesinde öğrencilerin %92'si tüm paketi alarak çalışıyor.
MATH 211 • Midterm I
Linear Algebra
Dorukhan Özcan
1799 TL
MATH 211 • Midterm II + Final
Linear Algebra
Dorukhan Özcan
1999 TL
Konular
Ch 3.3: Cramer's Rule, Adjoint and Applications
Cramer's Rule
Exam like Question 1
Exam like Question 2
Adjoint of a Matrix I
Adjoint Matrix II
Area of Triangle & Volume of Tetrahedron
Ch 4.1: Vector Spaces and Subspaces
Vector Spaces and Subspaces 1
Vector Spaces and Subspaces 2
Matrix Spaces & Matrix Subspaces
Polynomial 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
Ch 4.2: Null, Column and Row Spaces
Bases for Col A & Row A & Null A
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Ch 4.3: Bases, Linearly Independent Sets
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
Ch 4.4-5: Coordinate Systems
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
Ch 4.4-5: Coordinate Systems for Matrices
Coordinate Systems: Matrices 1
Coordinate Systems: Matrices 2
Coordinate Systems: Matrices 3
Coordinate Systems: Matrices 4
Ch 4.6: Change of Basis
Change of Basis: Vector Spaces
Change of Basis: Polynomials
Change of Basis: Matrices
Kernel and Range of Transformations
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
Transformations and Change of Basis
Transformation Matrix Relative to Basis 1
Transformation Matrix Relative to Basis 2
Transformation Matrix Relative to Basis 3
Exam like Question 1
Exam like Question 2
Exam Practice Problems: Part I
Basis for Subspaces
Vector Spaces and Subspaces
Basis & Dimension
Basis and Linear Dependence
Rank, Column and Null Spaces
Rank, Column and Null Spaces
Rank, Column and Null Spaces
Null & Column & Row Spaces
Null & Column & Row Spaces
Rank & Nullity
Rank & Nullity
Linear Transformation
Isomorphism
Polynomial Basis
Polynomial Basis
Polynomial Basis
Change of Coordinate Matrix
Cramer's Rule
Ch. 5.1-2: Eigenvalues and Eigenvectors
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
Ch. 5.3: Diagonalization
Diagonalization 1
Diagonalization 2
Exam like Question
Ch. 5.5: Complex Eigenvalues
Complex Eigenvalues I
Complex Eigenvalues II
Ch 6.1: Orthogonality
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
Ch 6.2: Orthogonal Sets and Bases
Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Orthonormal Sets and Basis
Orthogonal Matrix
Ch 6.3: Orthogonal Projections
Orthogonal Projection 1
Orthogonal Projection 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Ch 6.4: The Gram-Schmidt Process
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
QR Factorization
QR Factorization
Exam like Question
Ch.6.5: Least Squares Solution
Least Squares Solution
Exam like Question 1
Exam like Question 2
(NEW) Ch.6.7: Inner Product Space
Inner Product Space
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam Practice Problems: Part II
Diagonalization 1
Diagonalization 2
Diagonalization 3
Diagonalization 4
The Gram-Schmidt Process
The Gram-Schmidt Process
The Gram-Schmidt Process
The Gram-Schmidt Process
QR Factorization
QR Factorization
Sınav Provası: Spring 2024 Exam Problems
Polynomial Basis
Change of Basis
Eigenvectors & Diagonalization
Least Square Solution
Gram-Schmidt Process
(NEW) Sınav Provası: Fall 2024 Exam
Row Space & Column Space
Change of Coordinates Matrix
Eigenvalues & Eigenspaces
Linear Transformations
Complex Eigenvalues
QR Factorization
Least Square Solution
Inner Product
General Review Problems
Eigenvalues, Eigenspaces and Diagonalization I
Eigenvalues, Eigenspaces and Diagonalization III
Linear Transformations & Diagonalization
Linear Transformations & Diagonalization
Kernel and Range of Transformations
Kernel and Range of Transformations
Kernel and Range of Transformations
Kernel and Range of Transformations
Kernel and Range of Transformations
Linear Transformation & Change of Basis
Linear Transformation & Change of Basis
Orthogonal Complements
Orthogonal Complements
Gram-Schmidt Process
Gram-Schmidt Process
Gram-Schmidt Process
Değerlendirmeler
Çok iyi
Ders İçeriği
Ch 3.3: Cramer's Rule, Adjoint and Applications
Cramer's Rule
Exam like Question 1
Exam like Question 2
Adjoint of a Matrix I
Adjoint Matrix II
Area of Triangle & Volume of Tetrahedron
Ch 4.1: Vector Spaces and Subspaces
Vector Spaces and Subspaces 1
Vector Spaces and Subspaces 2
Matrix Spaces & Matrix Subspaces
Polynomial 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
Ch 4.2: Null, Column and Row Spaces
Bases for Col A & Row A & Null A
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Ch 4.3: Bases, Linearly Independent Sets
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
Ch 4.4-5: Coordinate Systems
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
Ch 4.4-5: Coordinate Systems for Matrices
Coordinate Systems: Matrices 1
Coordinate Systems: Matrices 2
Coordinate Systems: Matrices 3
Coordinate Systems: Matrices 4
Ch 4.6: Change of Basis
Change of Basis: Vector Spaces
Change of Basis: Polynomials
Change of Basis: Matrices
Kernel and Range of Transformations
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
Transformations and Change of Basis
Transformation Matrix Relative to Basis 1
Transformation Matrix Relative to Basis 2
Transformation Matrix Relative to Basis 3
Exam like Question 1
Exam like Question 2
Exam Practice Problems: Part I
Basis for Subspaces
Vector Spaces and Subspaces
Basis & Dimension
Basis and Linear Dependence
Rank, Column and Null Spaces
Rank, Column and Null Spaces
Rank, Column and Null Spaces
Null & Column & Row Spaces
Null & Column & Row Spaces
Rank & Nullity
Rank & Nullity
Linear Transformation
Isomorphism
Polynomial Basis
Polynomial Basis
Polynomial Basis
Change of Coordinate Matrix
Cramer's Rule
Ch. 5.1-2: Eigenvalues and Eigenvectors
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
Ch. 5.3: Diagonalization
Diagonalization 1
Diagonalization 2
Exam like Question
Ch. 5.5: Complex Eigenvalues
Complex Eigenvalues I
Complex Eigenvalues II
Ch 6.1: Orthogonality
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
Ch 6.2: Orthogonal Sets and Bases
Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Orthonormal Sets and Basis
Orthogonal Matrix
Ch 6.3: Orthogonal Projections
Orthogonal Projection 1
Orthogonal Projection 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Ch 6.4: The Gram-Schmidt Process
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
QR Factorization
QR Factorization
Exam like Question
Ch.6.5: Least Squares Solution
Least Squares Solution
Exam like Question 1
Exam like Question 2
(NEW) Ch.6.7: Inner Product Space
Inner Product Space
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam Practice Problems: Part II
Diagonalization 1
Diagonalization 2
Diagonalization 3
Diagonalization 4
The Gram-Schmidt Process
The Gram-Schmidt Process
The Gram-Schmidt Process
The Gram-Schmidt Process
QR Factorization
QR Factorization
Sınav Provası: Spring 2024 Exam Problems
Polynomial Basis
Change of Basis
Eigenvectors & Diagonalization
Least Square Solution
Gram-Schmidt Process
(NEW) Sınav Provası: Fall 2024 Exam
Row Space & Column Space
Change of Coordinates Matrix
Eigenvalues & Eigenspaces
Linear Transformations
Complex Eigenvalues
QR Factorization
Least Square Solution
Inner Product
General Review Problems
Eigenvalues, Eigenspaces and Diagonalization I
Eigenvalues, Eigenspaces and Diagonalization III
Linear Transformations & Diagonalization
Linear Transformations & Diagonalization
Kernel and Range of Transformations
Kernel and Range of Transformations
Kernel and Range of Transformations
Kernel and Range of Transformations
Kernel and Range of Transformations
Linear Transformation & Change of Basis
Linear Transformation & Change of Basis
Orthogonal Complements
Orthogonal Complements
Gram-Schmidt Process
Gram-Schmidt Process
Gram-Schmidt Process
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.