MATH 211 • Tüm Sınavlar • Linear Algebra
Özyeğin Üniversitesi MATH 211 (Linear Algebra) Midterm I sınavına hazırlık paketi.
İşlenen konular: Systems of Linear Equations, Vector Equations, Matrix Equations & Solution Sets of Linear Systems, Linear Independence, Matrix Operations and Inverse of a Matrix, Linear Transformation, The Matrix of a Linear Transformation, Determinant and Properties.
Ayda 1266 TL, peşin fiyatına 3 taksit
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.
Konular
Ch 1.1-2: Systems of Linear Equations
4 konu anlatımı · 5 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
Exam like Question 5
Ch 1.3: Vector Equations
6 konu anlatımı · 5 soru
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
4 konu anlatımı · 7 soru
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
1 konu anlatımı · 5 soru
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
6 konu anlatımı · 10 soru
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
18 soru
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
2 konu anlatımı · 2 soru
Linear Transformations 1
Linear Transformation 2
Exam like Question 33
Exam like Question 34
Ch1.9: The Matrix of a Linear Transformation
1 konu anlatımı · 1 soru
Matrix of a Linear Transformation
Exam like Question 35
Ch 3.1-2: Determinant and Properties
4 konu anlatımı · 7 soru
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
6 soru
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
4 soru
Span of Vectors & Linear Independence
Invertibility of a Matrix
Determinant & Co-factor Expansion
Linear Transformations
(NEW) Spring 2024 Exam Problems
5 soru
Existence and Uniqueness
Invertibility of a Matrix
Span of Vectors
Matrix Operations
Linear Transformations
(NEW) Fall 2024 Exam Problems
4 soru
Vector Equations
The Matrix of a Linear Transformation
Inverse of a Matrix
Determinant
Unicourse Special Review Problems
12 soru
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
Ch 3.3: Cramer's Rule, Adjoint and Applications
4 konu anlatımı · 2 soru
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 4.3: Bases, Linearly Independent Sets
3 konu anlatımı · 5 soru
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
2 konu anlatımı · 5 soru
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
4 konu anlatımı
Coordinate Systems: Matrices 1
Coordinate Systems: Matrices 2
Coordinate Systems: Matrices 3
Coordinate Systems: Matrices 4
Ch 4.6: Change of Basis
3 konu anlatımı
Change of Basis: Vector Spaces
Change of Basis: Polynomials
Change of Basis: Matrices
Kernel and Range of Transformations
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
Exam Practice Problems: Part I
28 soru
Determinants 1
Determinants 2
Determinant & Co-factor Expansion
Properties of Determinants 1
Properties of Determinants 2
Properties of Determinants 3
Properties of Determinants 4
Cramer's Rule
Adjoint Matrix
Basis for Subspaces
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Null, Column, and Row Spaces
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
Isomorphism
Polynomial Basis
Polynomial Basis
Change of Coordinate Matrix
Cramer's Rule
Transformations and Change of Basis
3 konu anlatımı · 2 soru
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
Ch. 5.1-2: Eigenvalues and Eigenvectors
6 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
Ch. 5.3: Diagonalization
2 konu anlatımı · 1 soru
Diagonalization 1
Diagonalization 2
Exam like Question
Ch. 5.5: Complex Eigenvalues
2 konu anlatımı
Complex Eigenvalues I
Complex Eigenvalues II
Ch 6.1: Orthogonality
3 konu anlatımı · 4 soru
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
4 konu anlatımı
Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Orthonormal Sets and Basis
Orthogonal Matrix
Ch 6.3: Orthogonal Projections
2 konu anlatımı · 3 soru
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
2 konu anlatımı · 2 soru
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
QR Factorization
1 konu anlatımı · 1 soru
QR Factorization
Exam like Question
Ch.6.5: Least Squares Solution
1 konu anlatımı · 2 soru
Least Squares Solution
Exam like Question 1
Exam like Question 2
(NEW) Ch.6.7: Inner Product Space
1 konu anlatımı · 3 soru
Inner Product Space
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam Practice Problems: Part II
10 soru
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
5 soru
Polynomial Basis
Change of Basis
Eigenvectors & Diagonalization
Least Square Solution
Gram-Schmidt Process
Sınav Provası: Fall 2024 Exam
8 soru
Row Space & Column Space
Change of Coordinates Matrix
Eigenvalues & Eigenspaces
Linear Transformations
Complex Eigenvalues
QR Factorization
Least Square Solution
Inner Product
General Review Problems
15 soru
Eigenvalues, Eigenspaces and Diagonalization I
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