MATH 211 • Midterm II + III • Linear Algebra
“çok memnun kaldım”
Onur Muratoğlu
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.
Kerem Başol
Eğitmen
2019 senesinde Koç Üniversitesi Matematik bölümüne başladım. Geçtiğimiz senelerde Calculus ve Linear Algebra derslerinde Tutor ve Teaching Assistant pozisyonlarında görev aldım. Halen Koç Üniversitesi Matematik ve Bilgisayar Mühendisliği çift anadal programını 4.00/4.00 ortalamayla fakülte birincisi olarak sürdürüyorum. Trigonometrik fonksiyonların elips üzerinde nasıl tanımlanabileceğini merak etmemle başlayan Matematik tutkumu aktarmak için Unicourse Matematik Zümresine katıldım.
Unicourse Garantisi
Bu dersi alma kararını senin için kolaylaştıralım. Eğer memnun kalmazsan 30 gün içinde bize ulaş, 3'ten fazla içerik tamamlamadıysan iade alabilirsin. Koşullar
Paketi Tamamla
🎓 MEF Üniversitesi öğrencilerinin %92'si tüm paketi alarak çalışıyor.
Konular
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
Exam-like Question 4
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
Basis for Subspaces (Null, Column, Row Spaces)
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Exam like Question
Basis for General Subspaces
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Basis for Polynomial Subspaces 2
Coordinate Systems (Vectors, Polynomials)
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
Orthogonality and Orthogonal Complement
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
Orthogonal Sets and Bases
Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Orthonormal Sets and Basis
Orthogonal Matrix
Basis for Orthogonal Complement
Orthogonal Projection
Orthogonal Projection 1
Orthogonal Projection 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
The Gram-Schmidt Process
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
Angle Between Vectors for a Given Inner Product
Linear Transformation
Linear Transformations 1
Linear Transformation 2
Matrix of a Linear Transformation
Inverse of Linear Transformation 1
Inverse of Linear Transformation 2
Linearity of Transformations
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Kernel and Range of Transformations
Basis for Kernel and Range of a Transformation 1
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
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
Diagonalization
Diagonalization 1
Diagonalization 2
Exam like Question 1
Exam like Question 2
Exam Practice Part I
Span of Vectors
Span of Vectors
Span of Vectors
Span of Vectors
Span of Vectors
Linear Independence
Linear Independence
Linear Independence
Linear Independence
Exam Practice Part II
Rank and Nullity - Theoretical
Null & Column & Row Spaces 1
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3
Null & Column & Row Spaces 4
Null & Column & Row Spaces 5
Column, Null and Row Spaces 1
Column, Null and Row Spaces 2
Column, Null and Row Spaces 3
Basis for Subspaces (Vectors)
Basis for Subspaces (Vectors)
Basis for Subspaces (Vectors)
Basis for Subspaces (Vectors)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Polynomials)
Basis for Subspaces (Polynomials)
Basis for Subspaces (Polynomials)
Basis for Subspaces (Polynomials)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Polynomials)
Spanning Sets (Polynomials)
Spanning Sets (Polynomials)
Spanning Sets (Matrices)
Linear Independence of Polynomials
Exam Practice Part III
Linear Transformation 1
Linear Transformation 2
Matrix of Linear Transformation 1
Matrix of Linear Transformation 2
Inverse of Linear Transformation 1
Inverse of Linear Transformation 2
Inverse of Linear Transformation 3
Composite of Linear Transformation 1
Reflection of a Transformation 1
Reflection of a Transformation 2
Reflection of a Transformation 3
Basis for Kernel and Range 1
Basis for Kernel and Range 2
Basis for Kernel and Range 3
Basis for Kernel and Range 4
Basis for Kernel and Range 5
Basis for Kernel and Range 6
Transformations & Change of Basis 1
Transformations & Change of Basis 2
Transformations & Change of Basis 3
Transformations & Change of Basis 4
Transformations & Change of Basis 5
Transformations & Change of Basis 6
Transformations & Change of Basis 7
Transformations & Change of Basis 8
Eigenvalues
Eigenvalue Eigenvector Diagonalizable
Diagonalization 1
Diagonalization 2
Diagonalization 3
Diagonalization 4
Diagonalization 5
Transformations & Eigenvalues 1
Transformations & Eigenvalues 2
Transformations & Eigenvalues 3
Transformations & Eigenvalues 4
Eigenvalue and Null Space
(New) Spring 2024 Exam Problems (Midterm 2)
Determinant
Basis and Coordinate
Rank, Null and Column Space
Subspace, Rank and Null Space
(New) Spring 2024 Exam Problems (Midterm 3)
Orthogonal Complement
Linear Transformation
Vector Projection
Orthogonal Vectors
Orthogonal Complement
Diagonalization
Değerlendirmeler
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
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
Exam-like Question 4
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
Basis for Subspaces (Null, Column, Row Spaces)
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Exam like Question
Basis for General Subspaces
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Basis for Polynomial Subspaces 2
Coordinate Systems (Vectors, Polynomials)
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
Orthogonality and Orthogonal Complement
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
Orthogonal Sets and Bases
Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Orthonormal Sets and Basis
Orthogonal Matrix
Basis for Orthogonal Complement
Orthogonal Projection
Orthogonal Projection 1
Orthogonal Projection 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
The Gram-Schmidt Process
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
Angle Between Vectors for a Given Inner Product
Linear Transformation
Linear Transformations 1
Linear Transformation 2
Matrix of a Linear Transformation
Inverse of Linear Transformation 1
Inverse of Linear Transformation 2
Linearity of Transformations
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Kernel and Range of Transformations
Basis for Kernel and Range of a Transformation 1
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
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
Diagonalization
Diagonalization 1
Diagonalization 2
Exam like Question 1
Exam like Question 2
Exam Practice Part I
Span of Vectors
Span of Vectors
Span of Vectors
Span of Vectors
Span of Vectors
Linear Independence
Linear Independence
Linear Independence
Linear Independence
Exam Practice Part II
Rank and Nullity - Theoretical
Null & Column & Row Spaces 1
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3
Null & Column & Row Spaces 4
Null & Column & Row Spaces 5
Column, Null and Row Spaces 1
Column, Null and Row Spaces 2
Column, Null and Row Spaces 3
Basis for Subspaces (Vectors)
Basis for Subspaces (Vectors)
Basis for Subspaces (Vectors)
Basis for Subspaces (Vectors)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Matrices)
Basis for Subspaces (Polynomials)
Basis for Subspaces (Polynomials)
Basis for Subspaces (Polynomials)
Basis for Subspaces (Polynomials)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Vectors)
Spanning Sets (Polynomials)
Spanning Sets (Polynomials)
Spanning Sets (Polynomials)
Spanning Sets (Matrices)
Linear Independence of Polynomials
Exam Practice Part III
Linear Transformation 1
Linear Transformation 2
Matrix of Linear Transformation 1
Matrix of Linear Transformation 2
Inverse of Linear Transformation 1
Inverse of Linear Transformation 2
Inverse of Linear Transformation 3
Composite of Linear Transformation 1
Reflection of a Transformation 1
Reflection of a Transformation 2
Reflection of a Transformation 3
Basis for Kernel and Range 1
Basis for Kernel and Range 2
Basis for Kernel and Range 3
Basis for Kernel and Range 4
Basis for Kernel and Range 5
Basis for Kernel and Range 6
Transformations & Change of Basis 1
Transformations & Change of Basis 2
Transformations & Change of Basis 3
Transformations & Change of Basis 4
Transformations & Change of Basis 5
Transformations & Change of Basis 6
Transformations & Change of Basis 7
Transformations & Change of Basis 8
Eigenvalues
Eigenvalue Eigenvector Diagonalizable
Diagonalization 1
Diagonalization 2
Diagonalization 3
Diagonalization 4
Diagonalization 5
Transformations & Eigenvalues 1
Transformations & Eigenvalues 2
Transformations & Eigenvalues 3
Transformations & Eigenvalues 4
Eigenvalue and Null Space
(New) Spring 2024 Exam Problems (Midterm 2)
Determinant
Basis and Coordinate
Rank, Null and Column Space
Subspace, Rank and Null Space
(New) Spring 2024 Exam Problems (Midterm 3)
Orthogonal Complement
Linear Transformation
Vector Projection
Orthogonal Vectors
Orthogonal Complement
Diagonalization
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