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Linear Algebra Topics

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1. Linear Equations with Matrices

1.1

Notation of matrices

1.2

Solving systems of linear equations by graphing

1.3

Representing linear system as a matrix

1.4

The three types of matrix row operations

1.5

Solving a linear system with matrices using Gaussian elimination

1.6

Row reduction and echelon forms

1.7

Linear combination and vector equations in

R^n

1.8

Matrix equation Ax=b

1.9

Solution sets of linear systems

1.10

Application of linear systems

2. Linear Transformation

2.1

Linear independence

2.2

Image and range of linear transformations

2.3

Properties of linear transformation

2.4

The matrix of a linear transformation

3. Matrix Operations

3.1

Adding and subtracting matrices

3.2

Multiplying a matrix by a scalar

3.3

Multiplying a matrix by another matrix

3.4

Zero matrix

3.5

Identity matrix

3.6

Properties of matrix addition

3.7

Properties of matrix scalar multiplication

3.8

Properties of matrix to matrix multiplication

4. Determinant of a Matrix

4.1

The determinant of a 2 x 2 matrix

4.2

The determinant of a 3 x 3 matrix (General & Shortcut Method)

4.3

Properties of determinants

4.4

Solving linear systems using Cramer's Rule

5. Inverse of Matrices

5.1

2 x 2 invertible matrix

5.2

The inverse of a 2 x 2 matrix

5.3

Solving linear systems using 2 x 2 inverse matrices

5.4

The inverse of a 3 x 3 matrices with matrix row operations

5.5

The invertible matrix theorem

6. Subspace of $\Bbb{R}^n$

6.1

Properties of subspace

6.2

Column space

6.3

Null space

6.4

Dimension and rank

7. Eigenvalue and Eigenvectors

7.1

Eigenvalues and eigenvectors

7.2

The characteristic equation

7.3

Diagonalization

7.4

Complex eigenvalues

7.5

Discrete dynamical systems

8. Orthogonality and Least Squares

8.1

Inner product, length, and orthogonality

8.2

Orthogonal sets

8.3

Orthogonal projections

8.4

Least-squares problem

8.5

Applications to linear models

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Linear Algebra Made Clear

Build understanding from concrete examples to abstract theory

Expert Video Solutions

Complete Practice System

24/7 AI Problem Helper

Linear Algebra Topics

Help

1. Linear Equations with Matrices

2. Linear Transformation

3. Matrix Operations

4. Determinant of a Matrix

5. Inverse of Matrices

6. Subspace of $\Bbb{R}^n$

7. Eigenvalue and Eigenvectors

8. Orthogonality and Least Squares

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Our approach aligns with the evidence

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Courses

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More

Linear Algebra Made Clear

Build understanding from concrete examples to abstract theory

Expert Video Solutions

Complete Practice System

24/7 AI Problem Helper

Linear Algebra Topics

Help

1. Linear Equations with Matrices

2. Linear Transformation

3. Matrix Operations

4. Determinant of a Matrix

5. Inverse of Matrices

6. Subspace of Rn\Bbb{R}^nRn

7. Eigenvalue and Eigenvectors

8. Orthogonality and Least Squares

Show All

Our approach aligns with the evidence

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6. Subspace of $\Bbb{R}^n$