Homogeneous Systems & Parametric Form Of Equations

In this video, I am discussing the Homogeneous Systems & Parametric form of equations. Its importance in Data Science and Machine learning.   You will also need an understanding of Row Reduced Echelon Form -- 

https://youtu.be/sNbMTfLT9n8

In this session, we will be continuing our discussion on Spans and Consistency  

Link to the previous discussion can be found here - https://youtu.be/yx_uKDEWF6c 

Augmented matrix is discussed in this video -https://youtu.be/gd9l5GUTUD8 

Row Reduced Echelon Form (RREF) - https://youtu.be/sNbMTfLT9n8

In this video, we will be discussing  

1. Properties of the matrix-vector  product 

2. Matrix Equations & Vector Equations 3.Multiple ways for writing the system of linear equations 

4. One more way for finding the value for the equation Ax =b

In this video, we will be discussing the following topics. 

1.  Linear Combination of Vectors 

2.  Vector Equations 

3.  Different representation techniques of linear systems. 

4.  Overview of Augmented matrix representation for vector equations.  

5.  Linear Span

In this video, I have discussed the following topics 

1. Finite dimension vector space 

2. Fields 

3. Finite & Infinite fields 

4. Vector spaces 

5. Subspaces

We will be discussing vectors in short. 

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In line with our discussion about matrices, this video covers some more kinds of matrices  

• Symmetric Matrix. 
• Skew- Symmetric Matrix. 
• Orthogonal Matrix 
• Permutation Matrix 
• Normal Matrix 
• Hermitian Matrix 
• Skew Hermitian Matrix 
• Unitary Matrix 
• Idempotent Matrix 
•  Projection Matrix 
•  Submatrix of a Matrix

Matrices discussion continued Part II -

Covers the following topics  

• Matrix transpose 
• Conjugate transpose 
• Matrix addition  
• Matrix multiplication with scalar and a matrix  
• Matrix properties 
• Inverse of matrix  
• Left Inverse and right inverse
• Calculating the inverse of 2X2 matrix

This video covers the following topics 

• What is a matrix? 
• Linear equation representation of the matrix. 
• Different kinds of matrix

This video covers ways in which we can solve linear equations represented in the form of a matrix.   I am discussing the following forms

• Row Echelon Form (REF),
• Gauss elimination method,
• Row Reduced Echelon Form (RREF) & Gauss Jordan elimination method.

This video explains linear equations representation in the form of matrices. Once the linear equations are represented as matrices we can identify whether the equation has a single solution, infinitely many solutions, or no solution.

We are discussing straight line equations. How to find the number of solutions for a straight-line equation.