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If AB = Ba, then matrix B is called commutative matrix of matrix A. try to find the condition that commutative matrix of matrix A should satisfy. A = 1101 A=1 1 0 1
B seems to be a generalized inverse of A
Such a simple matrix, you set B = a, B, C, D to calculate it
B=
a b
c d
AB =
a+c b+d
c d
BA=
a a+b
c c+d
AB = ba
a= a+c ==> c=0
b=b+d ==> d=0
d=c+d ==> c=0
Therefore, C = D = 0 is enough
So the second line of B is 0
What is the rank of multiplication of two full rank matrices with different ranks?
The matrix B obtained by crossing a line from matrix A asks what is the relationship between the ranks of a and B, and explains the reason
R (a) = R (b) or R (a) = R (b) + 1
Let the row vector group of a be A1, A2,..., am
If the first line is crossed out, then the group of line vectors of B is A2,..., am
If A1 can be expressed linearly by A2,..., am,
Then the row vectors of a and B are equivalent, where R (a) = R (b)
If A1 cannot be expressed linearly by A2,..., am
Then the maximally independent group of A2,..., am plus vector A1 constitutes a maximally independent group of A1, A2,..., am
Then R (a) = R (b) + 1
The welding height of the butt welding of two iron plates is 3mm in our factory. What tools do you need to measure
Is the iron plate butt joint form or hand over form (not clear)? Generally, if there is no special mark, it is calculated by (multiply by 0.7) (of course, it depends on the thickness and technical requirements of the steel plate), and the calculated data is the welding height you need
What tools are needed: steel ruler is used to calculate data. There are also two kinds of weld measurement tools. It's very simple to calculate without tools
What are the strange scenes of nature
Mirage
If the square of X is the square of 5xy + 6y, what is the ratio of X to y
x^2-5xy+6y^2=0
(x-2y)(x-3y)=0
X-2y = 0 or x-3y = 0
X / y = 2 or 3
Let a and B be any two nonzero matrices satisfying AB = 0, then there must be ()
A. A's column vector group is linearly related, B's row vector group is linearly related, B. A's column vector group is linearly related, B's column vector group is linearly related, C. A's row vector group is linearly related, B's row vector group is linearly related, d. A's row vector group is linearly related, B's column vector group is linearly related
Method 1: let a be m × n matrix, B & nbsp; Let AB = o know: R (a) + R (b) ≤ n, and let a and B be non-zero matrices, then: there must be rank (a) > 0, rank (b) > 0, it can be seen that: rank (a) < n, rank (b) < n, that is, the column vector group of a is linearly related, and the row vector group of B is linearly related, so: A. method 2: let AB = o know: every column of B is a solution of AX = 0, and ∵ B is a non-zero matrix, ax = 0 exists Similarly, from ab = O, btat = O, there is linear correlation of column vector group of BT, so row vector group of B is linear correlation, so a is selected
As shown in the figure, in △ ABC, ∠ BAC = 80 °, ab = AC, point P is a point in △ ABC, and ∠ PBC = 10 °, PCB = 30 °,
Verification: ∠ PAB = ∠ APB
There is a method that can be proved, but it will be more troublesome. Extend CP to intersect AB at point D, and make a vertical line from C to AB to intersect AB at point e. from the meaning of the topic, we can get: ∠ BPC = 140, ∠ ABP = ∠ DPB = 40, ∠ ADC = 80. So the triangle ADC is isosceles triangle, let AE be length 1, then de = 1, there is cosine theorem, we can get the length of AC, ab = AC
Given the function f (x) = 3x / 2x + 3, the sequence {an} satisfies A1 = 1, an + 1 = f (an), n ∈ n*
Prove that sequence (1 / an) is arithmetic sequence
a(n+1)=f(an)=3an/(2an+3)
1/a(n+1)=(2an+3)/(3an)=2/3+1/an
1/a(n+1)-1/an=2/3
So the sequence {1 / an} is an arithmetic sequence
How to judge whether vectors are collinear?
Collinear vector I'm not good at learning this fast, and I can't do a problem. What are the knowledge points involved in this fast?
Don't bother
A(x1,y1),B(x2,y2),C(x3,y3)
Vector (AB) = k * vector (BC) as long as it is true
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