In this post, we are going to talk about the Null space and solving linear system equations by using the null space.Null spaceLet A be a matrix whose columns are [a1, a2, ..., an].The equation is as follows:AX = 0 ; N(A) = {X | AX = 0}.We can interpret this intuitively: when matrix A multiplies a vector X and the result is zero, those X vectors form the null space. This means that the null space..

In this post, we are going to talk about the Vector space. Vector spaceA vector space is a set of vectors. A vector space must satisfy 3 conditions as follows:Let x, y be elements in V.x + y is in V (closed under addition)kx is in V for any scalar k (closed under scalar multiplication)the origin vector (0) is in VConclusion: if k1x + k2y is in V for any scalars k1, k2, then we call V a vector s..

Today, we are going to discuss the three types of Linear System Equations (LSE). When the number of unknowns is equal to the number of equations, it is called a Square System. We can represent it as: A(n×n) X = b In this system, the solution is usually unique, but exceptions can exist. If the number of unknowns is greater than the number of equations, it is called an Under-constrained System.We..

Today, we are going to talk about Gauss Elimination and Gauss–Jordan Elimination, which are crucial for solving linear equations. We discussed Gauss Elimination in the previous post. First of all, when GE is performed, the matrix is converted into Row Echelon Form. The next step is back substitution, which means going upward in the matrix to solve for the variables. On the other hand, when GJ is..

Gaussian elimination(GE)를 이용해 linear equation의 해를 구할 수 있다.하지만, 이 과정을 컴퓨터 프로그래밍으로 계산하기 위해서는 행렬로 표현할 수 있어야 한다. 이때 사용하는 방법을 알아보자. 1. Elementary matrixLet A be the original matrix. 이런 조건에서 첫 번째 행을 상수배하여 두 번째 행에 더하거나 빼는 과정을 하게 된다. 이러한 연산 과정을 행렬로 나타낸 것을 E21이라고 한다. E21은 identity matrix에서 (2,1) 위치에 상수를 넣어 만든 행렬이다. 또 다른 예시로는 E32가 있다. 이 행렬은 identity matrix의 (3,2) 위치에 coefficient를 넣은 행렬이다.Elementary matri..

What means linear? 1. f(x1 + x2) = f(x1) + f(x2) 2. f(cx1) = cf(x1) So, we are using this formula which equation meets linearlity f(ax1 + bx2) = af(x1) + bf(x2)