Finding the rank of matrix in linear algebra Let ABC be three matrices of order n, and | ab | is not equal to 0 R（ABC）=?R(A) ,R(ABC)=?R(C),R(ABC)=?R(B),R(ABC)=?R(AB)

Finding the rank of matrix in linear algebra Let ABC be three matrices of order n, and | ab | is not equal to 0 R（ABC）=?R(A) ,R(ABC)=?R(C),R(ABC)=?R(B),R(ABC)=?R(AB)

Let me analyze: | ab ≠ 0, that is, AB is reversible (take AB as a whole) so that R (ABC) = R (c) or R (CAB) = R (c) the others are uncertain & nbsp; see the fourth in the formula

A problem of linear algebra A is a matrix of m x n type, B is a matrix of order n. if the rank of B is n, then what is the rank of AB?

The rank of AB is the rank of A
prove:
Method 1:
Using the inequality of rank,
r(A)+r(B)-N

In linear algebra, let a be equal to the rank of matrix A and B be equal to the rank of transpose of matrix A. why is a equal to B?

This is the property of the rank of a matrix
Rank of a = rank of row vector group of a = rank of column vector group of a
If a is regarded as the rank of row vector group of a, then B is the rank of column vector group of a, so they are equal
Please accept if you are satisfied^_^

1137.7 billion yuan, the approximate value of the two significant figures retained by the rounding method is () billion yuan a.1 × 10 quartic power B

Is 1.1 × 10 to the fourth power
Choose a

It takes 80 seconds to build a 456 meter long bridge, and 77 seconds to build a 399 meter long tunnel at the same speed

Lie equation
Let X be the length of the train and y be the speed
x+456=80y
x+399=77y
The solution is x = 1064
y=19
The train is longer than the bridge

If the length and width of a rectangle are increased by 5 cm, the area will be increased by 105 square cm
I just surf the Internet. I hope you can help me write the process

Let the length and height be x and Y respectively
(x+5)（y+5）-xy=105
xy+5x+5y+25-xy=105
5(x+y)+25=105
5(x+y)=80
x+y=16
The perimeter of the original rectangle is 16 × 2 = 32 cm

How to calculate the fractional power of a fraction? For example, 27 / 125 ^ 2 / 3

27 / 125, square first and then square, or square first and then square third. The first operation is simple, and the result is 9 / 25

Xiao Hong in Chicago calls her aunt in Paris at 7:00 local time. Is that ok

It depends on whether it's 7:00 a.m. or 7:00 p.m. 7:00 a.m. is not suitable, because Paris is 3:00 p.m. and it can be at night, because Paris is 3:00 p.m. at that time

In rectangular paper ABCD, ab = 3, ad = 5, as shown in the figure, fold the paper so that point a falls on a on the edge of BC
In rectangular paper ABCD, ab = 3, ad = 5, fold the rectangular paper as shown in the figure, so that point B falls on point F on the edge of AD, and the crease is Eq. when point F moves on the edge of AD, the end points E and Q of the crease also move. If the limiting points E and Q move on AB and BC respectively, the maximum distance that point F can move on the edge of ad is Eq

(1) When Q coincides with D, as shown in Figure 1,
∵ quadrilateral ABCD is a rectangle, ad = 5, ab = 3,
∴BC=AD=5,DC=AB=3,∠C=90°,
From the folding, we know that a1'd = ad = 5,
In RT △ a1cd, according to Pythagorean theorem, a1'c2 + DC2 = a1'd2, a1'c2 = a1'd2-dc2 = 52-32 = 16,
∵A1'C＞0,
∴A1'C= 16 =4；
（2）
When a'is on the leftmost side of BC, Q coincides with D. at this time, from (1), a'c = 4,
When P and B coincide, a'2 in Figure 2 is on the rightmost side of BC,
At this point, we know from the folding: a'2b = AB = 3, then a'2c = 5-3 = 2, a 'should move between a'1 and a'2,
The maximum distance a 'can move on the edge of BC is ca'1-ca'2 = 4-2 = 2

Xiao Ming bought pencils and pens for 24 yuan, of which 0.5 yuan for each pencil and 5 yuan for each pen. He bought 21 pencils in total. How many pencils did he buy?
Suppose Xiao Ming bought x pencils. According to the meaning of the question, he can make out the formula

0.5x + 5 (21-x) = 24 solution x = 18, bought x pencils with 0.5x yuan, bought (21-x) pencils, spent 5 (21-x) yuan, a total of 24 yuan, so 0.5x + 5 (21-x) = 24 solution x = 18, so bought a total of 18 pencils