The problem of finding adjoint matrix The form of adjoint matrix is A11 A21 A31 A12 A22 A32 A13 A23 A33 Why not A11 A12 A13 A21 A22 A23 A31 A32 A33 In addition, if the transpose of determinant is equal to the original determinant, what is the relationship between the transpose of matrix and the original matrix?

The main purpose of adjoint matrix is: AA * = |a|e
If defined according to the second method, a of the above formula will be transposed
The transpose of determinant is equal to the original determinant
The relation between matrix transpose and original matrix is only row column exchange, because matrix is a number table, and there is no similar equal relation between them

Let a be a 3 * 3 matrix and a * be the adjoint matrix of A. if | a | = 2, find | a|
A=｜A｜A^(-1)
|A|=||A|A^(-1)|=|A|^3|A^(-1)|
=|A|^2=4
In general, if a is a square matrix of order n, there is a a = (n-1)
I want to ask why | a * | = | a | a ^ (- 1) | = | a | ^ 3 | a ^ (- 1) | in this step, if you remove that value, there will be a cubic
Novice, please explain in detail, thank you!

It's like this:
If a is a matrix of order n, for any number k, Ka means that all elements of matrix A are multiplied by K
Consider the determinant | Ka | in which each row has a common factor K, which is proposed (one for each row)
So | Ka | = k ^ n | a |
So in your question | a * | = | a ^ (- 1) | = | a ^ ^ 3 | a ^ (- 1)|

The length of the generatrix of the cone is 8, the radius of the bottom surface is 2, and a is a point on the circumference of the bottom surface. Starting from a, wrap a rope around the side of the cone and then return to a, then the shortest rope is?

The arc length is 4 π, the center angle is 4 π × 180 / 8 π = 90 degree
This fan-shaped string is the shortest length of the rope = 8 √ 2

The simple operation of decimal addition and subtraction is exactly the same as that of integer addition and subtraction

Yes

If the perimeter ratio of circle a to circle B is 2:3, the area ratio of circle a to circle B is 2:3______ ．

2 π R: 2 π r = 2:3, that is, R: r = 2:3, π R2: π R2 = R2: R2 = 22:32 = 4:9. Therefore, if the perimeter ratio of circle a and circle B is 2:3, the area ratio of circle a and circle B is 4:9

Take the sides AC and ab of △ ABC as one side, make square ABDE and acfg to the outside of triangle respectively, connect eg, and make ah ⊥ BC through point a
At H point, extend ha to intersect eg at m point

Ij is made through a, parallel to BC, and vertical lines are drawn from G and e to ij respectively, and the intersection points are I and J
Angle gam + angle CAH = angle gam + angle Gai = 90 degrees, so angle CAH = angle Gai
Angle AIG = angle AHC = 90 degrees, AC = AG
So △ AHC is equal to △ AIG, so AI = ah
Similarly, AJ = ah, so AI = AJ
Because GI, EJ and Ma are perpendicular to ij, AI = AJ
So am is the middle line of trapezoidal gije, so EM = GM
It's hard work, not a bit!

The chord length is 13167,
I don't have a calculator

R=10.832
S=19.191748
Do it yourself

Xiao Ming added one of the continuous natural numbers 1,2,3,. One more time, and the sum is 149. How small is the added number

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16=136
149-136=13
The number is 13
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In Lu Xun's from BaiCaoYuan to Sanwei bookstore, that word is used to describe abundance or enjoyment

Dripping

It is known that the inverse proportion function y = K / X and the primary function y = ax + B. when x = 2, the values of the two functions are - 2, and when x = 1, the values of the two functions are opposite to each other. The relationship between the two functions is obtained

Y1 = K / 2 = - 2, k = - 4
y2=2a+b=-2...(1)
y2=a+b=-y1=-k/1=4...(2)
(1) (2), a = - 6, thus B = 10
That is, Y1 = - 4 / X
y2=-6x+10
Substituting x = (y2-10) / (- 6) into Y1
y1=24/(y2-10)