MAT 112 • Midterm • Lineer Cebir

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

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

Inverse of a Matrix 1

Inverse of a Matrix 2

Practice Problem 1

Practice Problem 2

Practice Problem 3

Practice Problem 4

Elementary Matrix

Inverse of Elementary Matrix

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

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

LU Decomposition I

LU Decomposition II

LU Decomposition III

LU Decomposition (Alternatif)

LU Decomposition (Alternatif)

LU Decomposition (Alternatif)

Gaussian Elimination

Gaussian Elimination

Gaussian Elimination

Existence and Uniqueness 1

Existence and Uniqueness 2

Existence and Uniqueness 3

Existence and Uniqueness

Existence and Uniqueness 3

Matrix Operations

Matrix Operations

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

Solving systems with Inverse 3

Solving systems with Inverse 4

Elementary Matrices

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 I

Adjoint Matrix II

Adjoint Matrix III

Adjoint Matrix IV

Adjoint Matrix V

Cramer's Rule I

Cramer's Rule II

Exam like Question 1

Exam like Question 2

Area of Triangle & Volume of Tetrahedron

Equation of a Line and Plane

Determinant and Invertibility

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

Cramer's Rule

Cramer's Rule

Cramer's Rule

Inverse Matrix using Cofactor Expansion

Theory Problem 1

Theory Problem 2

Theory Problem 3-4

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

Vector Spaces and Subspaces

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

Exam like Question 7

Exam like Question 8

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

Null Space & Column Space & Row Space

Bases for Col A & Row A & Null A

Exam like Question

Basis for Vector Subspaces

Basis for Matrix Subspaces

Basis for Polynomial Subspaces

Basis for Polynomial Subspaces 2

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

Linear Transformations 1

Linear Transformation 2

Matrix of a Linear Transformation

Linearity of Transformations

Inverse of Linear Transformation 1

Inverse of Linear Transformation 2

Linear Transformations

Linear Transformations

Linear Transformations

Linear Transformations

Linear Transformation

Linear Transformation

Inverse of Linear Transformation

Inverse of Linear Transformation

Composite of Linear Transformation

Reflection of a Transformation

Reflection of a Transformation

Reflection of a Transformation

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

Basis for Kernel and Range

Basis for Kernel and Range

Basis for Kernel and Range

Basis for Kernel and Range

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

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

Transformations & Change of Basis 9