Using n-order Vandermonde determinant to calculate the answer Calculation by using n-order Vandermonde determinant The first line is a B C The second line is a ^ 2 B ^ 2 C ^ 2 The third line is B + C + A + B

r1+r3=
a b c
a^2 b^2 c^2
a+b+c a+b+c a+b+c
=(a+b+c)*
1 1 1
a b c
a^2 b^2 c^2
=(a+b+c)(c-a)(c-b)(b-a)

How to express matrix transpose in MATLAB

Conj is conjugate, just one more time-
The simple way I know is to add 'after the matrix variable to represent the transpose operation

How to find matrix transpose in MATLAB

>> A=[1 2 3;4 5 6]
A =
1 2 3
4 5 6
>> B=A'
B =
1 4
2 5
3 6

Matlab matrix transpose matrix, what is the function?

Matrix transpose is represented and implemented by the symbol "'"
For example: a = [1 2 3; 4 5 6; 7 8 9];
B=A` ↙
B=1 4 7
2 5 8
3 6 9
If Z is a complex matrix, then Z 'is their complex conjugate transpose matrix, and Z.' or conj (Z ') is used for non conjugate transpose matrix
size(a)
[D1, D2, D3,...] = size (a) find the size of the matrix. For m * n two-dimensional matrix, the first is the number of rows m and the second is the number of columns n;
For multidimensional matrices, the nth is the length of the nth dimension
Cat (k, a, b) matrix merge, run a = magic (3)
b = pascal(3)
c = cat(4,a,b)
Change 4 to 3 or 2 or 1, and realize the effect after combination
K = 1, the merged form is like [a; b], and the matrix is added to the row (the number of columns of a and B must be equal to merge);
K = 2, the merged form is like [a, b], the column is added with matrix (the number of rows of a and B is required to be equal to merge), and so on, the n-dimensional matrix merging requires the number of n-1 dimensions to be equal to merge)
Flip LR (a) matrix left and right
Flip up and down of flip (a) matrix
rot90(a)
The rot90 (a, K) matrix is rotated 90 degrees counter clockwise
The k parameter is defined as a 90 * k degree counterclockwise rotation
For example, when k = 1, rows (up and down) flip; when k = 2, columns (left and right) flip
tril(a)
The lower triangular part of tril (a, K) matrix (including diagonal elements) corresponds to the number of values when k = 0
When k parameter is set to positive and negative value, the diagonal line moves up or down to divide the lower triangular elements
triu(a)
The upper triangular part of tril (a, K) matrix (including diagonal elements) corresponds to the number of values when k = 0
When k parameter is set to positive and negative value, the diagonal line moves up or down to divide the upper triangular elements
diag(a)
Diag (a, K) generates diagonal matrix or takes out diagonal elements, corresponding to the number of values when k = 0
When k parameter is set to positive or negative value, the diagonal line moves up or down K rows to get diagonal elements or generate diagonal matrix
Repmat (a, m, n) matrix copy, the matrix A as a unit calculation, copy into m * n matrix, each element contains a matrix A, the actual result is a size (a, 1) * m row, size (a, 2) * n column matrix
w=meshgrid(s,t)
[u, v] = meshgrid (s, t) generates two matrices of order M = size (T, 1) * size (T, 2) and column n = size (s, 1) * size (s, 2)), where u is the n matrix elements of s in row order, m rows are repeated in column order, and V is the M matrix elements of T in column order, n columns are repeated in row order. When only one matrix is generated, w = U
eye(a)
Eye (a, K) generates unit square matrix of order a
The k parameter is set to generate a × k-order unit matrix, that is, after generating A-Order unit matrix, the first k columns are taken, which is insufficient to make up 0
ones(a)
One (a, K) generates all one square matrix of order a
All 1 matrix of order a × K is generated by setting k parameter
zeros(a)
Zeros (a, K) generating all zero square matrix of order a
All zero matrix of order a × K is generated by setting k parameter
Inv (a) generates the inverse matrix of a

Is the value formula of trigonometric determinant the same as upper triangle and lower triangle?

Same

Please help to prove the trigonometric determinant of determinant whose elements below the main line are all 0. Its value is the same as the diagonal determinant~

This can be explained by the definition of determinant
Every term in the definition of determinant is the product of n elements, which are located in different rows and columns of determinant
Therefore, the first column can only take a11, after that, the first row and the first column can not take other elements. For convenience, you can cross out the first row and the first column
Similarly, column 2 can only take A22
In turn, n elements can only take a11, A22,..., Ann
So the determinant is equal to the product of n elements on the main diagonal
The trigonometric determinant whose elements below the leading line are all 0 has the same value as the diagonal determinant

One angle in a triangle is two-thirds of the second angle. The third angle is 30 ° larger than the sum of the two angles. Find the degree of the three angles

Let the second angle be X
2(x+2/3x)+30=180
X = 45 degrees
The first angle is 30 degrees, the second 45 degrees and the third 105 degrees

One angle of a triangle is two thirds of the second angle. The third angle is 30 degrees larger than the sum of the two angles. Find the degree of the three angles

Let a corner = X
2(x+2/3x)+30=180
x=45
2/3x=30
30+45+30=105

The degree of an angle and the length of the opposite side are known. The range of the other side of a triangle with one solution and two solutions is obtained
If the title.. seek to explain!

Let ABC, B = α, AC = B,
BC is free length. The relation between ab = C and B is discussed
1. Let ∠ C = 90 ° and B = csin α, C = B / sin α have a unique solution
2. There is no solution when C > b / sin α
3. There are two solutions when B < C < B / sin α
4. There is a unique solution when C ≤ B

A triangle tells the length of each side and the degree of an angle. How to find the area of the triangle?

In a right triangle, the ratio of the opposite side to the oblique side of ∠ a (non right angle) is called ∠ a

Using n-order Vandermonde determinant to calculate the answer Calculation by using n-order Vandermonde determinant The first line is a B C The second line is a ^ 2 B ^ 2 C ^ 2 The third line is B + C + A + B