It is known that square matrix A of order n satisfies a square = 0. It is proved that e + 3a is invertible and its inverse matrix is obtained

It is known that square matrix A of order n satisfies a square = 0. It is proved that e + 3a is invertible and its inverse matrix is obtained

(E+3A)(E-3A)=E-9A^2=E

The difference between tangent vector and normal vector in Higher Mathematics?

In higher mathematics, the tangent vector is generally used to find a curve, and the normal vector is used to find a plane. The tangent vector can be found by derivative, and the normal vector can be found by writing the general equation of the plane

Two teachers of a school take some students to travel. The price of company a and company B is 100 yuan. The discount of company a and company B is as follows:
The preferential condition of company a is that one teacher charges in full, and the rest teachers and students charge at a 7.50% discount; the preferential condition of company B is that all teachers and students charge at a 20% discount
How should the teacher choose to save money?

Let all teachers and students be X,
The cost of company a is 100 + 100 × 0.75 (x-1) = 75X + 25,
The cost of company B is 100 × 0.8 × x = 80x,
If 75X + 25 = 80x, then x = 5,
When x is 5, the cost of both companies is the same,
When x is less than 5, company B saves money,
When x is greater than 5, company a saves money

When Lim tends to zero, e ^ x-e ^ - 1 / X

The limit of 0 / 0 type and ∞ / ∞ type can be determined by using the method of Rhoda: LIM (1 + x-e ^ x) / X (0 / 0 type) x → 0 = LIM (1-e ^ x) / 2x (or 0 / 0 type) x → 0 = LIM (- e ^ x) / 2 (already fixed) x → 0 = - 1 / 2

The function f (x) = log2x-1 defined on [1,64], the function g (x) = - F2 (x) + F (x3) (1) find the domain of definition of function g (x); (2) find the maximum value of function g (x) and the corresponding value of x when taking the maximum value

(1) From the known conditions, we can get 1 ≤ x ≤ 641 ≤ x3 ≤ 64, we can get 1 ≤ x ≤ 4, so the definition field of function g (x) is [1,4] (4 points) (2) ∵ g (x) = − (log2x − 1) 2 + log2x3 − 1 = − log22x + 5log2x − 2 = − U2 + 5u − 2 = − (U − 52) 2 + 174 = ϕ (U), X ∈ [1,4], u = log2x

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The area of a classroom is about 50 square meters, 200 such classrooms are about 1 hectare. How to calculate?
A football field covers an area of about 7000 square meters, and 140 football fields cover an area of about 1 square kilometer. How to calculate this?

1 square kilometer = 1 000 000 square meters, 7 000 × 140 = 980 000 ≈ 1 000 000 square meters
So 140 of these football fields are about one square kilometer

If the image of power function y = f (x) passes through point (2,4), then f (1 / 2)?

4=2^a
Power exponent a = 2
f(1/2)=1/4

Look up English words
What does mark mean

They put a new product on the market

Known arithmetic sequence {an}, A10? SN

(1) S6 = S4 and S6 = S4 + A5 + A6
So A5 + A6 = 0
Because of the arithmetic sequence {an}, A10, and because A5 + A6 = 0
So a 50
So when n = 5, S5 is the smallest
(2) Because A5 + A6 = 0
So a1 + A10 = 0
So S10 = (a1 + A10) * 10 / 2 = 0
So when n = 10, S10 = 0
So when n0