-How to judge whether this matrix is similar to diagonal matrix or not

-How to judge whether this matrix is similar to diagonal matrix or not

Let the eigenvalue of the matrix a be λ
be
|A-λE|=
-3-λ 1 -1
-7 5-λ -1
-6 6 - 2 - λ line 1 minus line 2
=
4-λ λ-4 0
-7 5-λ -1
-6 6 - 2 - λ column 2 plus column 1
=
4-λ 0 0
-7 2-λ -1
-6 0 -2-λ
=(4-λ)(2-λ)(-2-λ)=0
The solution is λ = 4,2 or - 2
This matrix has three different eigenvalues, so it must be similar to diagonal matrix

Can the following matrices be similar to diagonal matrices? If a can be similar to diagonal matrices, then the invertible matrix P is obtained so that p-1ap is diagonal?
1. The matrix is composed of four elements, the first is 3,4, the second is 5,2
2. A matrix of 9 elements, the first behavior 5, - 3,2
Second behavior 6, - 4,4
Third behavior 4, - 4,5
That is to say, how to calculate the eigenvalues, eigenvectors, eigenroots and so on in detail
How to deduce from these that can be similar to diagonal matrix,

1. Yes. A has two different eigenvalues: 7, - 2
2. Yes. A has three different eigenvalues: 1,2,3

Matrix calculation
A is a two-dimensional array of 3x3 cells;
B is a one-dimensional array of 3x1 cells;
Find the generalized inverse of x such that ax-b = 0
What does this sentence mean?

Are you sure you want to find the generalized inverse of X? You should find the generalized inverse of A

Calculate the following matrix
[0 1 0] [1 2 3] [1 0 2]
[1 0 0] ^2012 * [0 4 5] * [0 1 0] ^2012
[0 0 1] [-1 6 7] [0 0 1]

It is easy to conclude that a ^ 2 = 4E
Therefore, when n = 2K, a ^ n = a ^ (2k) = (a ^ 2) ^ k = (4e) ^ k = 4 ^ Ke = 2 ^ ne
When n = 2K + 1, a ^ n = a ^ (2k) a = (4e) ^ Ka = 4 ^ Ka = 2 ^ (n-1) a
Are you satisfied with the above answers?

3a-2 [2B + 1 / 2 (a-b)] to help solve,

Given that z = a + I / 1 + 3I is a pure imaginary number, then the real number a is equal to?

z=a+i/1+3i=(a+i)(1-3i)/(1+3i)(1-3i)=(a-3ai+i+3)/10=[(a+3)-(3a-1)i]/10
When a + 3 = 0, z = a + I / 1 + 3I is a pure imaginary number, so a = - 3

The fruit shop shipped 200 kg of apples, 20% more pears than apples, and 75% of bananas. How many kg of bananas?

Pear = 200 × (1 + 20%) = 240 kg
Banana = 240 △ 75% = 320 kg

1 * 2 * 1 / 3 plus 2 * 3 * 1 / 4 + One fourth of 48 * 49 * 50 is equal to using primary school knowledge

=(1/2)×(1/1×2+1/2×3)+(1/2)×(1/2×3-1/3×4)+…… +(1/2)×(1/48×49-1/49×50)
=(1/2)×(1/1×2+1/2×3+1/2×3-1/3×4+…… +1/48×49-1/49×50)
=(1/2)×(1/1×2-1/49×50)
=306/1225

Is Kirchhoff's law still valid if the voltage source in the circuit diagram for verifying Kirchhoff's law is changed into a current source? Is it changed into a controlled source?

Kirchhoff's law is actually the relationship between node current and mesh voltage. Just grasp the voltage and current characteristics of each element. For the controlled source, one of the voltage or current can be known according to the relationship, and then another variable can be introduced to solve the problem by listing an amplifier. In fact, Kirchhoff's law is also applied

A middle school plans to organize seventh grade teachers and students to carry out patriotic education activities
A middle school plans to organize seventh grade teachers and students to carry out patriotic education activities
Dialogue with Xiao Fang and Xiao Ming about car rental:
Mr. Li: "Ping An passenger transport company has two types of buses with 60 seats and 45 seats, each with 60 seats
The rent for one day is 200 yuan more than that for 45 seats. "
Xiao Fang: "the teachers and students of grade eight of our school rented 6 buses with 60 seats and 4 buses with 45 seats in this passenger transport company yesterday
The total rent for a day in Shaoshan is 8200 yuan. "
Xiao Ming: "our seventh grade teachers and students rent seven 60 seat and three 45 seat buses, which are just full."
(1) How much is the daily rental of 60 seat and 45 seat passenger cars of Ping An passenger transport company?
(2) According to the car rental scheme proposed by Xiao Ming, how much does the seventh grade teachers and students of the school need to rent a car in Ping'an company for one day
How much is the average cost per person? (accurate to 1 yuan)
Please make a list of answers

(1) 940 yuan for 60 seats and 740 yuan for 45 seats
(2) The rent is 21960 yuan
The average consumption is 16 yuan per person