MATH 227 • Tüm Sınavlar • Introduction to Linear Algebra
İhsan Doğramacı Bilkent Üniversitesi MATH 227 (Introduction to Linear Algebra) Midterm sınavına hazırlık paketi.
İşlenen konular: Gaussian Elimination, Matrix Operations and Inverse, Matrix Equations, Elementary Matrices, Determinants, Cramer's Rules, Adjoint Matrix, Vectors (Dot Product & Projections), Vector Spaces and Subspaces.
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
Gaussian Elimination
4 konu anlatımı · 5 soru
Augmented Matrix - Row Reduction 1
Augmented Matrix - Row Reduction 2
Existence and Uniqueness of Solution
Free Variables (or Parameters)
Exam-like Questions 1
Exam-like Questions 2
Exam-like Questions 3
Exam-like Questions 4
Exam like Question 5
Matrix Operations and Inverse
3 konu anlatımı · 6 soru
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
Exam like Question 4
Exam like Question 5
Exam like Question 6
Matrix Equations
3 konu anlatımı · 4 soru
Matrix Equation
Solving AX = B with Inverse
Invertible or not ?
Exam like Question 1
Exam like Question 2
Exam-like Question 3
Exam like Question 4
Elementary Matrices
2 konu anlatımı · 3 soru
Elementary Matrix
Inverse of Elementary Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Determinants
4 konu anlatımı · 7 soru
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant
Properties of Determinant 2
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
Cramer's Rules
1 konu anlatımı · 4 soru
Cramer's Rule 1
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Adjoint Matrix
4 konu anlatımı
Adjoint Matrix 1
Adjoint Matrix 2
Adjoint Matrix 3
Adjoint Matrix 4
Vectors (Dot Product & Projections)
3 konu anlatımı · 7 soru
Vectors: Arithmetic, Parallelism and Unit Vector
Angles between Vectors: Dot Product
Vector Projection
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
Vector Spaces and Subspaces
3 konu anlatımı · 6 soru
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
Sample Midterm Problems
27 soru
Row Reduction 1
Row Reduction 2
Consistent & Inconsistent Systems
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence and Uniqueness 4
Existence and Uniqueness 5
Matrix Operations 1
Matrix Operations 2
Inverse of a Matrix 1
Inverse of a Matrix 2
Inverse of a Matrix 3
Solving Systems with Inverse 1
Solving Systems with Inverse 2
Determinant and Invertibility 1
Determinant and Invertibility 2
Elementary Matrices 1
Elementary Matrices 2
Properties of Determinants 1
Properties of Determinants 2
Properties of Determinants 3
Properties of Determinants 4
Theory Problem 1
Theory Problem 2
Theory Problem 3-4-5
Theory Problem 6-7
Fall 2023 Exam Problems
7 soru
Row Reduction
Existence and Uniqueness
Inverse of a Matrix
Determinant
Properties of Determinant
Elementary Matrices
True-False Problems
Fall 2024 Exam Problems
4 soru
Existence and Uniqueness
Solving system with Inverse
Determinant
Subspaces or not ?
Vectors: Linear Combination and Span
7 konu anlatımı · 3 soru
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
3 konu anlatımı · 6 soru
Linear Independent Sets
Linear Independence of Matrices
Special Theorem for Matrix Equation
Exam-like Questions 1
Exam-like Questions 2
Exam-like Question 3
Exam-like Questions 4
Exam-like Questions 5
Exam-like Question 6
Vector Spaces and Subspaces
3 konu anlatımı · 7 soru
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
5 konu anlatımı · 4 soru
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
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Change of Basis Part I
5 konu anlatımı · 5 soru
Coordinate Systems: Introduction
Coordinate Systems: Polynomials
Coordinate Systems: Matrices 1
Coordinate Systems: Matrices 2
Coordinate Systems: Matrices 3
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam like Question 4
Exam like Question 5
Change of Basis Part II
3 konu anlatımı
Change of Basis: Vector Spaces
Change of Basis: Polynomials
Change of Basis: Matrices
Linear Transformations
3 konu anlatımı · 4 soru
Linear Transformations 1
Linear Transformation 2
Exam like Question 1
Exam like Question 2
Matrix of a Linear Transformation
Exam like Question 3
Exam-like Question 4
Transformations and Change of Basis
3 konu anlatımı · 7 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
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
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
Diagonalization
2 konu anlatımı · 2 soru
Diagonalization 1
Diagonalization 2
Exam like Question 1
Exam like Question 2
Orthogonality, Orthogonal Complement and Basis
4 konu anlatımı · 4 soru
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
Exam like Question 4
The Gram-Schmidt Process
2 konu anlatımı · 4 soru
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Angle Between Vectors for a Given Inner Product
Inner Product Spaces
1 konu anlatımı · 3 soru
Inner Product Space
Exam like Question 1
Exam like Question 2
Exam like Question 3
Cayley Hamilton Theorem
1 konu anlatımı · 2 soru
Cayley-Hamilton Theorem
Application of Cayley-Hamilton Theorem
Application of Cayley-Hamilton Theorem
Sample Final Part I
14 soru
Null & Column & Row Spaces 1
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3
Null & Column & Row Spaces 4 (Fall 2020)
Null & Column & Row Spaces 5
Column, Null and Row Spaces 6
Column, Null and Row Spaces 7
Null & Column & Row Spaces 8 (Fall 2021)
Diagonalization
Diagonalization
Diagonalization
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Sample Final Part II
17 soru
Span of Vectors
Span of Vectors
Span of Vectors
Span of Vectors
Span of Vectors
Linear Independence
Linear Independence
Linear Independence
Linear Independence
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Polynomials)
Spanning Sets (Polynomials)
Spanning Sets (Polynomials)
Spanning Sets (Matrices)
Sample Final Part III
16 soru
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
Theory Problems (Proof & True/False)
7 soru
Theory Problem 1
Theory Problem 2
Theory Problem 3
Theory Problem 4
Theory Problem 5
Theory Problem 6 (Spring 2022)
Theory Problem 7 (Spring 2022)
Fall 2023 Exam Problems
4 soru
Null & Column & Row Spaces
Basis and Subspaces
Diagonalization
Orthogonality and Change of Basis