The solution of diagonal matrix 2 0 1 3 1 3 Find his diagonal matrix and judge whether they are similar or not

The solution of diagonal matrix 2 0 1 3 1 3 Find his diagonal matrix and judge whether they are similar or not

|λ-2 0 -1 |
|-3 λ-1 -3|＝﹙λ-1﹚²﹙λ-6﹚
|-4 0 λ-5|
When λ = 1
|-1 0 -1|
|-3 0 -3|
|-The rank of 40 - 4 | is 1
The corresponding homogeneous equations have two linearly independent solutions, that is, λ = 1 has two linearly independent eigenvectors
So the original matrix A is similar to the diagonal matrix, that is, there is an invertible matrix P such that. P ^ (- 1) AP = diag (1,1,6)

This paper presents an algorithm for transforming 2 * 2 integer matrix into diagonal form

a b
c d
Line 2 - line 1 of C / a times
a b
0 d-bc/a
Line 1 - line 2 of B / (d-bc / a)
a 0
0 d-bc/a
If d-bc / A is not zero, the matrix can be diagonalized by elementary transformation. If d-bc / A is zero, the matrix is singular

On the smooth horizontal plane, there is a slider with mass M. on the left side of the slider is a smooth 1 / 4 arc with radius r = 1m. A small ball with mass m rushes up the slider with velocity V0 moving to the right. Given that M = 4m, G is 10 m / S2. If the small ball just doesn't jump out of the upper end of the arc, find:
(1) What is the initial velocity V0 of the ball? (2) what is the maximum velocity of the slider?
[how to judge the speed direction when the ball slides out of the slider]?

First, when the ball rushes up to the slider and reaches the highest point, the ball and the slider have the same velocity (horizontal direction), which is conserved by momentum: MV0 + 0 = (M + m) v

1 / 4 minus 1 / 6 of a number equals 120. Find the number

x/4-x/6=120.x=1440.

Force analysis of roller coaster
When the roller coaster reaches the highest point of the circle, how to express its centripetal force

Gravity support force (regarded as particle)
Centripetal force is combined with external force

If the equation (M2-1) x2 + (m-1) x + 3 = 0 is a linear equation of one variable with respect to x, then the value of M is ()
A. ±1B. 1C. -1D. 0

From the meaning of the question: M2-1 = 0, M-1 ≠ 0, the solution: M = - 1, so choose: C

A. The distance between B and a is 585km. A and B start from a and B and run in opposite directions. If they start at the same time, they will meet in 7.5h. If a drives for 7.5h, B will start again
Results the two vehicles met 2.5 hours after B set out,

Let the speed of car a be XKM / h and that of car B be YKM / h
According to the meaning of the title:
7.5(x+y)=585
7.5x+2.5(x+y)=585
The solution is: x = 52, y = 26

How much is 1-2 + 3-4 + 5-6 + 7-8 + 9-10 +. + 2001-2002?

-1001

Guess three idioms as follows: 1 * 1 = 1 dozen one idiom. 0 + 0 =? Dozen one idiom, the square of 1000 = 100 * 100 * 100 dozen one idiom

1. 10% will not change
2. Make something out of nothing
3. Do everything possible

Apple pear and orange 30 kg, three kinds of fruit 80 yuan, including apple 4 yuan, pear 3 yuan, orange 2 yuan, how many jin each of the three kinds of fruit?

Apple * 4 + orange * 3 + (30 apple orange) * 2 = 80, that is, orange = 20 Apple * 2. It is a binary linear Diophantine equation, with innumerable answers: Apple 0.5, 1,. 5.1,. 8.5,... 9 orange 19, 18,. 9.8,. 3,... 2 pear 10.5, 11,... 15.1,. 18.5,... 19 integer solutions are nine of them