Vector Expression of Outer Center, Inner Center, Center of Gravity and Vertical Center of Triangle VECTOR EXPRESSIONS OF THE PROPERTIES OF THE OUTER CENTER, INNER CENTER, CENTER OF GRAVITY AND PERPENDICULAR CENTER OF TRIANGLE

The outer center is the intersection of the vertical bisectors of the sides of the triangle, and the distance to each vertex is equal. The inner center is the intersection of the angular bisectors of each corner of the triangle, and the distance to the three sides is equal. The center of gravity is the intersection of the center lines of the three sides. The vertical center is the intersection of the three highs. As for the expression, you know these properties clearly. I hope it can help you,(__)(*...

Formulas of Plane Vector and Triangular Four Centers

The necessary and sufficient conditions for the linear independence of vector groups α1,α2,α3,αs are A.α1,α2,α3.αs are not zero vectors Any two vectors of B.α1,α2 and α3 are out of proportion. C.α1,α2, and α3.αs can not be linearly represented by the other S-1 vectors D.α1,α2,α3.αs must be orthogonal non-zero vector group The necessary and sufficient conditions for the linear independence of vector groups α1,α2,α3,αs are A.α1,α2,α3.αs are not zero vectors Any two vectors of B.α1,α2 and α3 are out of proportion. Any of the vectors C.α1,α2,α3.αs can not be linearly represented by the remaining S-1 vectors D.α1,α2,α3.αs must be orthogonal non-zero vector group The necessary and sufficient conditions for the linear independence of vector groups α1,α2,α3,αs are A.α1,α2,α3.αs are not zero vectors Any two vectors of B.α1,α2 and α3 are out of proportion. Any vector of C.α1,α2,α3.αs can not be linearly represented by the other S-1 vectors. D.α1,α2,α3.αs must be orthogonal non-zero vector group

Vector group A linear correlation, A=0? Linear uncorrelated, A not equal to 0? Such as title Linear correlation of vector group A, A=0? Linear uncorrelated, A not equal to 0? Such as title

The description of the problem is not strict. According to the meaning of the problem, vector group A is composed of n n-dimensional vectors, but A=0 appears in the problem. The estimate is that the determinant of the matrix composed of vector group A is equal to 0. Let A=(a1,a2,...,an) be a n*n matrix, then the necessary and sufficient condition for a1,a2,...,an linear correlation is |A|=0 or a1,...

The description of the problem is not strict. According to the meaning of the problem, vector group A is composed of n n-dimensional vectors, but A=0 appears in the problem. The estimation is that the determinant of the matrix composed of vector group A is equal to 0. Let A=(a1,a2,...,an) be a n*n matrix, then the necessary and sufficient condition a1,a2,...,an linear correlation is |A|=0 or a1,...

Is |A| equal to zero if vector group A is linearly related Where A is not necessarily a square matrix Is |A| equal to zero if vector group A is linearly related Where A is not necessarily a matrix

A is not a square matrix, there is no determinant.
If A is a square matrix, there must be |A|=0
Certificate:
Because you can do a basic row transformation, change a row to 0
I.e.
A1
A2
A3
...
An
Because there are k1,..., kn that are not all 0s so that
K1a1+k2a2+...+knan=0
Find a ki=0
You can multiply the first row by k1/ki, the second row by k2/ki..., the nth row by kn/ki and add to the ith row
The i-th row can be changed to 0. When calculating the row formula,|A |=0 can be obtained by expanding the i-th row.

Let β1=α1+α2,β2=α2+α3,β3=α3+α4,β4=α4+α1 proof vector group β1,β2,β3,β4 linear correlation

β1 - β2 + β3 - β4 = 0
So linear correlation

Vector Expression of Outer Center, Inner Center, Center of Gravity and Vertical Center of Triangle VECTOR EXPRESSIONS OF THE PROPERTIES OF THE OUTER CENTER, INNER CENTER, CENTER OF GRAVITY AND PERPENDICULAR CENTER OF TRIANGLE