Let a be a matrix of order n, satisfying AA ^ t = e (E is the identity matrix of order n), a ^ t be the transpose matrix of a, and | a|

Let a be a matrix of order n, satisfying AA ^ t = e (E is the identity matrix of order n), a ^ t be the transpose matrix of a, and | a|

E+A^T = (E+A)^T
Determinant on both sides
|E+A^T| = |(E+A)^T| = |E+A|

Derivation of important matrix formulas
From AA * = a * a = | a | e, we know: 1. | a * = | a | ^ (n-1) 2. (KA) * = k ^ (n-1) a * 3. (a *) * = | a | ^ (n-2) a

Proof: 1, it is clear that a and a * are matrices of the same order, so AA * AA * ? = ||||||a * |a * \||||||||\|\\124\\\\\\\124\\\\\\124\\\\\\\\\\\\\\\\so (KA) * = k ^ n | a | E / (KA) = k ^ (n-1) | a |

It seems that there is only the formula of the n-th power of the main diagonal block matrix in Teacher Liu's tutorial book. Is there a formula of the n-th power of the sub diagonal block matrix?
It seems that there is only the formula of the n-th power of the main diagonal block matrix in Teacher Liu's tutorial book. Is there a formula of the n-th power of the sub diagonal block matrix? For example
（O A ）^n
（B O）

There is no such thing as this one

Mr. Liu, is there a formula for the power of the main diagonal matrix? Here are two examples: (300 (2100400031005) 004) cube
(3 000 4 000 5)
The cube of (21003 10004)

Is this the cube of matrix determinant

Let the joint density function of (ξ, η) be used to find the distribution density function of (ξ + η)
Let the joint density function β of (ξ, η) be
1/4[1+xy(x^2-y^2)],｜x｜≤1,｜y｜≤1
P (x, y) = {0, other
And find the distribution density function of (ξ + η)?

F(y)=P{ξ+η

Given that the maximum value of the function y = asinx + B (a < 0) is 7 and the minimum value is - 3, find the value of ab

The maximum value of y = asinx + B (a < 0) is 7 and the minimum value is - 3
Then:
-a+b=7
a+b=-3
The sum of the two formulas is as follows:
b=2
The result of subtracting the two formulas is as follows:
a=-5
So: a = - 5, B = 2
ab=-10

What is four seventh times five thirds? Seven eighth times five thirds?

20／21.35／24

Rectangle, parallelogram, triangle and trapezoid in two parallel lines
The largest area is () the smallest area is () the equal area is () and ()
Draw the largest circle in a rectangle. The area of the circle is ()% of the area of the square
Draw the largest square in a circle. The area of the circle is () times that of the square

Because the width of rectangle is 1.5, the bottom of parallelogram is 1.4, the length of triangle is 3.2, the top of trapezoid is 1.8, and the bottom is 1.2
Therefore, the area of the rectangle is 1.5 * high
Parallelogram: 1.4 * high
Triangle: 1.6 * high
Trapezoid: 1.5 * high
The largest is a triangle, the smallest is a parallelogram, and the equal things are rectangles and trapezoids
2.78.5%
57 times

Given the line segments a, B and C, draw a line segment so that it equals 2b-a + C
——————— a
__________ b
________ c

Suppose a = 10, B = 8, C = 5
2b-a+c=2×8-10+5=11

Factorization factor 1-xn (one minus the nth power of x)
It seems that the result is: (1-x2) (1 + x2 + X3 + '+ X (n-1)), right

1-x^n=1^n-x^n=(1-x)[1+x+x^2+x^3+..+x^(n-1)]