It is proved that R is equivalent Let R be a binary relation on N * n, arbitrary, belonging to n * n R b=d. It is proved that R is equivalent Finding quotient set n * n / R

R B = D. then 1. R b = B holds, so the reflexive property satisfies 2. R b = D; R D = f, so if R, R, then B = D = f, then R, that is, the transitive property holds 3. R b = D, then r also holds, because d = B holds, so r is equivalent. This relationship shows that as long as the following B is the same, we regard it as one, with no a

Let R be a relation over n * n, which is defined as follows: (a, b) r (C, d) ad = BC
Let R be a relation over n * n, which is defined as follows: (a, b) r (C, d) ad = BC,
It is proved that R is equivalent

First, we prove Reflexivity: for any (a, a), AA = AA holds, so (a, a) r (a, a), (a, a) has reflexivity
In the proof of symmetry: ab = Ba holds for any (a, b), so (a, b) r (B, a), (a, b) has symmetry
Finally, we prove transitivity: for any a, B, C, ab = Ba, BC = CB, AC = Ca, so (a, b) r (B, a), (B, c) = (C, b), (a, c) r (C, a), (a, b), (B, c), (C, a) has transitivity
Do not know the answer is not correct, only for reference

Let a = {a, B, C}, B = {a, B} discrete mathematics ρ (a) - ρ (b) mean? How to calculate
The answer is {C}, {a, C}, {B, C}, {a, B, C}
ρ (b) - ρ (a) = empty set

I see. Let's see. There's C here
C is the result of a-b
In other words, C must have
And then it's going to take out the rest to make up for Liu
The rest is
{A,B}
A subset of this set is
{},{A},{B},{A,B}
Then add C

Matrix and transformation of graph position
Did a problem, first gave a plane rectangular coordinate system, there is a triangle, and then said that the matrix (- 10) represents
0 1
A kind of transformation (refers to the change of position, roughly refers to the translation type), let you describe in detail what kind of transformation is
Please explain me as a fool, I only know that matrix is matrix, at most can multiply inverse, do not know it can also represent the transformation of position

I think that since the topic is placed in the coordinate system, and there is a triangle, according to my understanding, it should be such a triangle, which has three vertices, and should give you the coordinates respectively, and then transform it into another triangle according to the matrix, assuming that one of the vertex coordinates is (x, y), then the matrix transformation should be (x, y) multiplied by (- 10) (0

Matrix and transformation the following matrix changes the given figure into what figure, and points out what the transformation is
(1)
The equation is y = 2x + 2
〔0 1〕
(2)
The curve equation is x ^ 2 + y ^ 2 = 4
(0 1)
(3)
(- 10) point a (2,5)
( 0 1)

1 unchanged
2 ellipse expansion into 0.25x ^ 2 + y ^ 2 = 4
3-point reflection transform (- 2.5)

Two dimensional graphic transformation matrix problem
Transform matrix using 2D graphics
2 0 0
0 1 0
1 1 1
What is the result of the transformation?

This must be agreed in advance, otherwise God knows how to change
The more likely case is Z = AZ, where a is the transformation matrix you give, z = [x, y, 1] 'is the original coordinate, and z = [x, y, 1]' is the new coordinate
In some places, it is customary to use row vector, that is Z '= z'a, which is equivalent to Z = a'z. so there must be ambiguity without prior agreement

Write the transformation matrix of the following figure transformation
1. Take (4,3) as the reference point, enlarge 3 times in X direction and 2 times in Y direction
2. Centrosymmetric transformation with (2,1) point as the center of symmetry;
3. Axisymmetric transformation with y = x + 8 as the axis of symmetry;
This is the problem of computer graphics

1. The original point m (x, y, 1) t, the transformed point m '(x', y ', 1) t, satisfies the relation X' = 3 (x-4), y '= 2 (Y-3) [30 - 12] the transformation matrix is a = [0 2 - 6] am = m' (the same below) [0 01] 2. The original point (x, y, 1), the transformed point (x ', y', 1), satisfies the relation X '+ x = 2 * 2, y' + y = 2 * 1, and obtains x '= 4-x

To find the inverse of a matrix, I know I can do it. Elementary row transformation is an identity matrix on the left and an identity matrix on the right
I want to ask: forget that the book says that only level 3 or above can do that, level 2 is OK

Second order is OK
But it's not necessary
A =
a b
c d
Then a ^ - 1 = [1 / (AD BC)]*
d -b
-c a
It's easy to remember: change the position of the main diagonal, change the sign of the secondary diagonal, and then divide the determinant | a |

Matrix column vector multiplication
The table is too deep. It's better to have an example

Column vector is a matrix with only one column, which can be used to express the multiplication rule of vector matrix. Simply put, the multiplication rule is as follows: if the left and right matrices are multiplied, the row of the matrix is the same as the left, and the column is the same as the right. The row is determined by the left, and the column is determined by the right

Let a be similar to B, and the eigenvalues of a are known to be 2,3,3. Then | B ^ - 1|=

Solution: the eigenvalues of similar matrices are the same
So the eigenvalues of B are 2,3,3
So | B | = 2 * 3 * 3 = 18
So | B ^ - 1 | = 1 / 18
Please accept if you are satisfied^_^

It is proved that R is equivalent Let R be a binary relation on N * n, arbitrary, belonging to n * n R b=d. It is proved that R is equivalent Finding quotient set n * n / R