Matrices Elimination

Matrices elimination (or solving system of linear equations) is the very first and fundamental skill throughout Linear Algebra. It's probably the first lesson of all sorts of courses.

Terminology

Matrix Transformation

It’s a subset of Linear transformation, just with higher dimension rules & multiple points graph multiplying together.

YOU BREAK THE RULE IN TO DIFFERENT UNIT VECTORS i, j, k... AND BREAK THE GRAPH INTO DIFFERENT POINTS, AND APPLY EACH i, j, k RULES TO EACH POINT.

Determinant of Transformation

It’s quite easy to calculate, and not too hard to understand what’s behind it.

The Determinant of a transformation is How much the AREA of the new Graph scaled.

Composition of Matrix Multiplication

Composition of Matrix Multiplication means More than one linear transformations applies to a graph one by one.

**Although you can see two matrices multiplying together as a transform applying to a graph.
But actually sometime you can see it…

Lecture note: MIT OCW 18.06 SC Unit 1.2 Elimination with Matrices

Elimination is the method EVERY softwares use to solve linear equations.

prerequisites:

• Terminology(Augmented matrix, elementary matrix, pivot, gauss elimination…)…

Lecture note: MIT OCW 18.06 SC Unit 1.4 Factorization into A = LU

Prerequisites

• Matrix Inverses |
• Matrix multiplication |
• Elementary Matrix |
• Permutation Matrix |

Column space of Matrix

Means The SET of all possible outputs a matrix.
In another word, it's THE SPAN OF THE COLUMNS OF THE MATRIX.

The columns of the matrix tell where the basis vectors land, like i & j.
And the span of all basis vectors gives you all…

Lecture note: MIT OCW 18.06 SC Unit 1.6Column Space and Nullspace