Using elementary transformation to find the inverse matrix: let a = 3 - 20 - 10 22 21 - 2 - 3 - 20 12 1 fast···

Using elementary transformation to find the inverse matrix: let a = 3 - 20 - 10 22 21 - 2 - 3 - 20 12 1 fast···

(A,E) =
3 -2 0 -1 1 0 0 0
0 2 2 1 0 1 0 0
1 -2 -3 -2 0 0 1 0
0 1 2 1 0 0 0 1
R1-3r3 (line 3 minus 3 times line 1)
0 4 9 5 1 0 -3 0
0 2 2 1 0 1 0 0
1 -2 -3 -2 0 0 1 0
0 1 2 1 0 0 0 1
r1-4r4,r2-2r4,r3+2r4
0 0 1 1 1 0 -3 -4
0 0 -2 -1 0 1 0 -2
1 0 1 0 0 0 1 2
0 1 2 1 0 0 0 1
r2+2r1,r3-r1,r4-2r1
0 0 1 1 1 0 -3 -4
0 0 0 1 2 1 -6 -10
1 0 0 -1 -1 0 4 6
0 1 0 -1 -2 0 6 9
r1-r2,r3+r2,r4+r2
0 0 1 0 -1 -1 3 6
0 0 0 1 2 1 -6 -10
1 0 0 0 1 1 -2 -4
0 1 0 0 0 1 0 -1
Exchange will do
1 0 0 0 1 1 -2 -4
0 1 0 0 0 1 0 -1
0 0 1 0 -1 -1 3 6
0 0 0 1 2 1 -6 -10

Let the matrix A = 1,0,2; 0,2,0; - 1,0,3, find a ^ - 1

1 0 2 1 0 0
0 2 0 0 1 0
-1 0 3 I 0 0 1
After elementary transformation
1 0 0 3/5 0 -2/5
0 1 0 0 1/2 0
0 0 1 1/5 0 1/5
That is, the left side is transformed into an element matrix by primary transformation, and the right side is its inverse matrix

Factorize the following formula into the square of (a + b) + A + B + 1 / 4

The original formula = (a + b) ² + (a + b) + 1 / 4
=(a+b)²+2×(1/2)×(a+b)+(1/2)²
=(a+b+1/2)²
Hope to adopt

In 2008, Xiaoming's mother deposited 5000 yuan in the bank for three years at an annual interest rate of 5.40%
Xiaoming's mother deposited 5000 yuan in the bank in 2008, fixed for three years, with an annual interest rate of 5.40% and an interest rate of 5%?

Should the tax rate be 5%?
5000 * 5.4% * 3 = 810 yuan (interest for three years)
810 * 5% = 40.5 yuan (amount of tax deduction required)
810-40.5 = 769.5 yuan (amount actually received after three years)
The sum of principal and interest is 5769.5 yuan, and the actual interest is 769.5 yuan

The total workload of group A's four workers in March is 20 pieces more than 4 times of the per capita quota of this month, and that of group B's five workers in March is 20 pieces less than 6 times of the per capita quota of this month. (1) if the per capita workload of two groups of workers in this month is equal, how many pieces is the per capita quota of this month? (2) If the actual per capita workload of group A is 2 pieces more than that of group B, what is the per capita quota of this month? (3) If the actual per capita workload of group A is 2 pieces less than that of group B, what is the per capita quota of this month?

Suppose that the per capita quota of this month is x, then the total workload of group A is (4x + 20), and the per capita workload is 4x + 204; the total workload of group B's five workers in March is less than 6 times of the per capita quota of this month, and the total workload of group B is (6x-20), and the per capita workload of group B is 6x − 205. (1) ∵ the per capita workload of the two groups is equal, ∵ 4x + 204 = 6x − 205, and the solution is: x = 45 The per capita quota is 45 pieces; (2) ∵ the per capita workload of group A is 2 pieces more than that of group B, ∵ 4x + 204 − 2 = 6x − 205, the solution is: x = 35, so the per capita quota of this month is 35 pieces; (3) ∵ the per capita workload of group A is 2 pieces less than that of group B, ∵ 4x + 204 = 6x − 205-2, the solution is: x = 55, so the per capita quota of this month is 55 pieces

"A three person team is randomly assigned from five employees of the sales and development department, four employees of the marketing department and one employee of the sales and finance department. Then the probability of one person in each of the three departments in the team is" excuse me

First of all, there are a total of C (lower 10, upper 3) ways to send out, because three people are sent out from 10 people, and the result is 120
Next, there are 20 ways to meet the requirements. There are 5 * 4 * 1 = 20 ways, because there are 5 ways, 4 ways and 1 way for each department to send one person
So the probability is 20 / 120 = 1 / 6

What is the difference between probability, frequency and frequency?

Put aside those tedious definitions, probability is the ideal thing, frequency is the real thing
For example, if you flip a coin 100 times, 56 times face up and 44 times face up, the frequency of the coin face up is 56 / 100, the frequency of the coin face up is 56, and the probability of the coin face up is still 1 / 2, which is ideal and will not be changed by the experimental results. It can be said that as long as the number of experiments is more, the frequency is closer to the probability

(3 / 4-1 / 2) * (1 / 3 + 1 / 4) simple,

(3 / 4 - 1 / 2) * (1 / 3 + 1 / 4)
=（3/4-2/4）x(4/12+3/12)
=1/4x7/12
=7/48

A ^ 3 = b * C ^ 2 is the mathematical relationship between expression B and C?
^2 is the square and ^ 3 is the cubic
If B = C, then a ^ 3 = C * C ^ 2 = C ^ 3, now B is not equal to C, what is the mathematical relationship between them?
In addition, if we only know a and know that B is not equal to C, can we use a to find B and C?
For example: a = 25, then 25 ^ 3 = 54 * 17 ^ 2
B = 54, C = 17
The above formula is only an example and is approximately equal
If we know C, and B is not equal to C, can we use C to find B and a?
Three must be greater than 0, longflied can you explain in detail how to deal with the logarithm on both sides

If all three numbers are greater than 0, then both sides take logarithm, and their relationship is very clear. If the three numbers are not greater than 0 at the same time, then a and B must have the same sign, otherwise there is no solution in the real number, and it will be changed into the case that all three numbers are greater than 0

How does 4 10 - 6 3 equal 24 and 3 - 5 7 - 13

10-(-6*3)-4=24
[(-5)*(-13)+7]/3=24