MATH 275 • Midterm • Linear Algebra
Atılım biz geldik! Math 275 dersi düşündüğün kadar zor değil; Dersimizdeki özet konu anlatımları ve kitabınızdaki bölüm sonu soru çözümleriyle konuyu öğrenecek, sonrasında son yılların çıkmış sınav sorularıyla antreman yapacaksın.
Tamamen senin okuluna özel hazırlanmış bu içerik akışıyla Lineer Cebir dersinden istediğin notu alacaksın. Bu dersimizde sunduğumuz içerikler sırasıyla: 1) Systems of Linear Equations 2) Row Reduction- Gaussian Elimination 3) Matrix Operations 4) Inverse of a Matrix 5) Solving systems with Inverse 6) Determinants 7) Properties of Determinants 8) Adjoint of a Matrix 9) Cramer's Rule 10) Vector Spaces and Subspaces
Eğitmen
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.
Paketi Tamamla
🎓 Atılım Üniversitesinde öğrencilerin %92'si tüm paketi alarak çalışıyor.
Konular
Systems of Linear Equations
Augmented Matrix - Row Reduction 1
Augmented Matrix - Row Reduction 2
Existence and Uniqueness of Solution
Free Variables (Free Parameter)
Practice Problem 1
Practice Problem 2
Practice Problem 3
Practice Problem 4
Practice Problem 5
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Operations with Matrices
Fundamental Matrix Operations
Practice Problem 1
Practice Problem 2
Practice Problem 3
Practice Problem 4
Practice Problem 5
Practice Problem 6
Practice Problem 7
Practice Problem 8
Practice Problem 9
The Inverse of a Matrix
Inverse of a Matrix 1
Inverse of a Matrix 2
Practice Problem 1
Practice Problem 2
Practice Problem 3
Practice Problem 4
Elementary Matrices
Elementary Matrix
Inverse of Elementary Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Matrix Equations (AX = B Formu)
Product of a Matrix and a Vector
Matrix Equation
Solving AX = B with Inverse
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Determinants
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant I
Properties of Determinant II
Exam like Question 1
Exam-like Question 2
Exam like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 5
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
Exam-like Question 9
Adjoint of a Matrix
Adjoint of a Matrix I
Adjoint Matrix II
Adjoint Matrix III
Adjoint Matrix IV
Adjoint Matrix V
Cramer's Rule
Cramer's Rule I
Cramer's Rule II
Exam like Question 1
Applications of Determinant
Area of Triangle & Volume of Tetrahedron
Equation of a Line and Plane
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 General Subspaces
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Basis for Polynomial Subspaces 2
Basis for Subspaces (Null, Column, Row Spaces)
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Exam like Question
Exam Practice Problems: Part I
Gaussian Elimination Method
Existence and Uniqueness 1
Existence and Uniqueness 2
Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
Solving systems with Inverse 1
Solving Systems with Inverse 2
Solving systems with Inverse 3
Determinant and Invertibility
Existence, Determinant and Invertibility 1
Existence, Determinant and Invertibility 2
Properties of Determinants 1
Properties of Determinants 2
Properties of Determinants 3
Properties of Determinants 4
Subspace or Not 1
Subspace or Not 2
Subspace or Not 3
Subspace or Not 4
Subspace or Not 5
Polynomial Subspace or Not 1
Polynomial Subspace or Not 2
Polynomial Subspace or Not 3
Exam Practice Problems: 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
(NEW) Summer 2024 Exam
True/False Statements
Inverse Matrix and Elementary Matrices
Linear System
Inverse Matrix
Cofactor Expansion
Cofactor
Subspace or Not
Subspace or Not
Linear System of Equations
Rank, Nullity, Row Space and Null Space
(NEW) Fall 2024 Exam
Question 1
Question 2
Question 3
Question 4
Question 5
Theory Problems
Theory Problem 1
Theory Problem 2
Theory Problem 3-4
Theory Problem 5-6
Theory Problem 7
Theory Problem 8
Theory Problem 9
Theory Problem 10
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
Systems of Linear Equations
Augmented Matrix - Row Reduction 1
Augmented Matrix - Row Reduction 2
Existence and Uniqueness of Solution
Free Variables (Free Parameter)
Practice Problem 1
Practice Problem 2
Practice Problem 3
Practice Problem 4
Practice Problem 5
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Operations with Matrices
Fundamental Matrix Operations
Practice Problem 1
Practice Problem 2
Practice Problem 3
Practice Problem 4
Practice Problem 5
Practice Problem 6
Practice Problem 7
Practice Problem 8
Practice Problem 9
The Inverse of a Matrix
Inverse of a Matrix 1
Inverse of a Matrix 2
Practice Problem 1
Practice Problem 2
Practice Problem 3
Practice Problem 4
Elementary Matrices
Elementary Matrix
Inverse of Elementary Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Matrix Equations (AX = B Formu)
Product of a Matrix and a Vector
Matrix Equation
Solving AX = B with Inverse
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Determinants
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant I
Properties of Determinant II
Exam like Question 1
Exam-like Question 2
Exam like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 5
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
Exam-like Question 9
Adjoint of a Matrix
Adjoint of a Matrix I
Adjoint Matrix II
Adjoint Matrix III
Adjoint Matrix IV
Adjoint Matrix V
Cramer's Rule
Cramer's Rule I
Cramer's Rule II
Exam like Question 1
Applications of Determinant
Area of Triangle & Volume of Tetrahedron
Equation of a Line and Plane
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 General Subspaces
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Basis for Polynomial Subspaces 2
Basis for Subspaces (Null, Column, Row Spaces)
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Exam like Question
Exam Practice Problems: Part I
Gaussian Elimination Method
Existence and Uniqueness 1
Existence and Uniqueness 2
Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
Solving systems with Inverse 1
Solving Systems with Inverse 2
Solving systems with Inverse 3
Determinant and Invertibility
Existence, Determinant and Invertibility 1
Existence, Determinant and Invertibility 2
Properties of Determinants 1
Properties of Determinants 2
Properties of Determinants 3
Properties of Determinants 4
Subspace or Not 1
Subspace or Not 2
Subspace or Not 3
Subspace or Not 4
Subspace or Not 5
Polynomial Subspace or Not 1
Polynomial Subspace or Not 2
Polynomial Subspace or Not 3
Exam Practice Problems: 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
(NEW) Summer 2024 Exam
True/False Statements
Inverse Matrix and Elementary Matrices
Linear System
Inverse Matrix
Cofactor Expansion
Cofactor
Subspace or Not
Subspace or Not
Linear System of Equations
Rank, Nullity, Row Space and Null Space
(NEW) Fall 2024 Exam
Question 1
Question 2
Question 3
Question 4
Question 5
Theory Problems
Theory Problem 1
Theory Problem 2
Theory Problem 3-4
Theory Problem 5-6
Theory Problem 7
Theory Problem 8
Theory Problem 9
Theory Problem 10