What is linear algebra? Graphically speaking, linear algebra deals with lines and their transformations. In short, linear algebra is linear transformation represented using vectors of numbers and matrices of two dimensional numbers.
We solve linear equations with unknown variables associated with each term of the linear equations. For example,
ax + by = c (linear equation)
Each term has unknowns (x, y) and coefficient (a, b) and equals a constant (c). Also, geometrically, each linear equation represents a straight line, hence, the name ‘linear’.
Imagine a few lines intersecting each other , then we could find the coordinates of intersections and we have a solution to the linear equations involved. Such equations form a system of linear equations which can solved using vectors and matrices. it is usually in the form of Ax = b.
Prerequisite To Learn Linear Algebra
The only prerequisite to learn linear algebra is basic algebra course and understanding of coordinate systems. This is because during our course we will have to apply concepts like exponents, solving equations by adding subtracting, multiplying with fractions,and so on.
If you know some programming, then its good idea to practice programming by creating programs for solution to linear equations. That’s totally up to you.
Topics From Linear Algebra
Here are the list of topics from linear algebra. You should read sequentially from top to bottom.
- System of Linear Equations
- Inconsistent Linear Systems
- Type of Matrices
- Elementary Row Operations
- Row-Echelon Form
- Gaussian Elimination
- Homogeneous System of Linear Equations
- Matrix Operations
- Matrix Addition
- Matrix Subtraction
- Matrix Multiplication
- Matrix Transpose
- Trace of Matrix
- Power of Matrices
- Inverse of Matrix
- Finding Inverse Matrix
- Inverse of Diagonal Matrix
- Inverse of Triangular Matrices
- Introduction to Determinants
- Finding Determinant By Cross Multiplications
- Finding Matrix of Minors
- Cofactors of Matrix
more topics coming soon …