Let a be a square matrix of order n and a * be the adjoint matrix of A. It is proved that N, R (a) = n, R (a *) = 1, R (a) = N-10, R (a)

Let a be a square matrix of order n and a * be the adjoint matrix of A. It is proved that N, R (a) = n, R (a *) = 1, R (a) = N-10, R (a)

When R (a) = n, a is reversible, | a | ≠ 0
AA * = | a | e, indicating that a * is reversible, R (a *) = n
When R (a) = n-1, a is irreversible, | a | = 0
AA * = |a|e = 0, so r (a *) = 1
So r (a *) = 1
When R (a)

Let a be a matrix of order n and | a | = 2, then | AA * + 2I|=____
Trouble master to write the process, just began to learn linear algebra is not very good at doing

Because AA * = |a|i = 2I
So | AA * + 2I | = | 4I | = 4 ^ n | I | = 4 ^ n

Cylinder formula

Cylinder formula
cylinder
v: Volume H: height s; bottom area R: bottom radius C: bottom perimeter
(1) Side area = perimeter of bottom surface × height
(2) Surface area = side area + bottom area × 2
(3) Volume = bottom area × height
(4) volume = side area △ 2 × radius

Use the multiplication rule to complete the table below. What rules can you find

It is known that the function f (x) = x2 + MX + LNX is a monotone increasing function, and the value range of M is ([method for finding the symmetry axis of derivative function]. M ≥ - 2 roots 2

∵f（x）=x2+mx+lnx
∴f′（x）=2x+m+1/x
The function f (x) = x2 + MX + LNX is monotonically increasing,
The results show that ∧ f ′ (x) = 2x + m + 1 / x > 0 is constant on (0, + ∞)
That is - M ≤ 2x + 1 / X is constant on (0, + ∞)
When x ∈ (0, + ∞), 2x + 1 / X ≥ 2, root sign 2
- M ≤ 2 root sign 2
That is, m ≥ - 2, root 2

8700mm cubic equals () cubic cm, thank you,

8.77

If a * b = 5A + 2b-1, the value of 3 * [(- 4) * 6] is
I'm going to school

(-4)*6=5*(-4)+2*6-1=-9;
3*【(-4)*6】=3*(-9)=5*3+2*(-9)-1=-4

Qing which expert to point out the sphere volume formula derivation process, thank you

1. The derivation of the volume formula of the ball: first, the plane of the ball center is used to intercept the ball, and the ball is divided into two hemispheres of equal size by the cross section. The cross section ⊙ is called the bottom surface of the hemisphere. (1) step 1: partition. Use a group of planes parallel to the bottom surface to cut the hemisphere into layers. (2) step 2: find the approximate sum

The astronomical unit light year is the distance that light travels in a year. Some stars are far away from us, some are hundreds of millions of light years old, and our eyes are organs that receive light. Can we understand that if a star is one billion light years away from us, that is to say, we see the star as it was one billion years ago, and we want to see it as it is now, it will take one billion years to see it?

Yes, it's like this. Let me give you an example: it takes eight minutes for the light emitted by the sun to reach the earth, so the light we see is just what the sun looked like eight minutes ago. But we also need to know that not all stars are like this, if there are other foreign materials (such as the strong gravity of black holes sucking light away, dust and other materials refracting light...) , which will darken the bright stars

Math problem 1 / 1 * 3 + 1 / 3 * 5 + 1 / 5 * 7 +... 1 / 97 * 99 + 1 / 99 * 101 =? Thank you!

0.5(1-1/3+1/3-1/5+1/5.-1/101)=0.5(1-1/101)=50/101