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A problem about matrix in linear algebra Let a be an M × n matrix and R (a) = R. it is proved that there exists an M × n matrix B with rank r and an R × n matrix C with rank r, such that a = BC
The order of B should be MXR, otherwise BC cannot be multiplied,
This problem is a construction problem,
For any m × n matrix A can be reduced to standard matrix form
That is, there are invertible matrices P of order m and Q of order n such that a = PVQ,
Where V = Er 0
0 0
Er is the identity matrix of order r, then the rank of V is r
Let B be PV, obviously the order of B is MXR, C is VQ, obviously the order of C is R × n
Since P and Q are invertible matrices, the rank of B and C is equal to the rank r of V
So BC = PV * VQ = PVQ = a
On the subject of linear algebraic matrix
1. Let N-order equation satisfy a ^ 3 + 2A ^ 2 + A-E = 0. Prove that matrix A is invertible and find a ^ (- 1)
2. Let n-order matrix a satisfy 3A (a-en) = a ^ 3. It is proved that the inverse matrix of en-a is (en-a) ^ 2
As long as ab = e can be explained, two matrices can be inversed, and each other is inverse matrix 1, a ^ 3 + 2A ^ 2 + A-E = 0, then a (a ^ 2 + 2A + e) = e, so a is invertible, the inverse matrix is a ^ 2 + 2A + E2, 3A (a-en) = a ^ 3, 3A ^ 2-3a = a ^ 3, that is 3A ^ 2-3a-a ^ 3 = 0 (en-a) (en-a) ^ 2 = (en-a) ^ 3 = en-3a + 3A ^ 2
If the price of a commodity is reduced by 10% according to the current price, it will still make a profit of 180 yuan. If the price is reduced by 20%, it will lose 240 yuan
It can be found that the price reduced by 10% is 180 yuan more than the cost
The price reduced by 20% is 240 yuan less than the cost
The difference between the two prices is 240 + 180 = 420
420 (90% - 80%) = 4200 yuan - cost
How many significant numbers are there in the power of 3.50 ^ 10?
There is something wrong with the writing
It should be 3.50 * 10 ^ 6
^It means power
According to what I wrote above, the significant numbers are 3, 5 and 0, accurate to 10000
According to what you wrote, it's the 10th power of 3.50 and the 6th power of 3.50, that is, the 60th power of 3.50. It can't be calculated
A mathematical algebra problem,
If (a-2b) (a-2b) = 9, (2a + b) (2a + b) = 25, find the square of a plus the square of B, the value of ab
Because the square of a-2b is 9, a-2b = 3
Because the square of 2A + B is 25, 2A + B = 5
Solution of a series of equations
b=-0.2
a=2.6
Then calculate a ^ 2 + B ^ 2 = 6.8
ab=-0.52
Why does abstract labor reflect the social relationship of commodity producers exchanging labor with each other
The value of goods can only be realized through exchange, and the essence of commodity exchange is labor exchange. Because every commodity is a labor product, labor exchange between commodity producers can be realized through commodity exchange
Abstract labor forms commodity value, so abstract labor also reflects labor exchange between commodity producers through commodity exchange
Of all the two digit numbers, there are () two digit numbers larger than ten digit numbers
A. 20B. 36C. 72D. 81
According to the meaning of the question, this question is a problem of classification and counting. Because the number of digits is greater than ten digits, there are 8 categories of digits: 2, 3, 4, 5, 6, 7, 8, 9. In each category, the two digits that meet the conditions are 1, 2, 3, 4, 5, 6, 7, 8, 1 + 2 + 3 + 4 + + 7 + 8 = 36
A math problem in the first grade of junior high school. I want to speed up the process. I want to finish it in 20 minutes
In the isosceles triangle, we know AB = 2x + 1, BC = 4x-1, CA = 7, find the perimeter of the isosceles triangle ABC
It's known that it's an isosceles triangle, so the two waists are equal. Then it's OK according to the given metric sequence. The key is to know which two are its waists, = it's OK to get up, and it's OK to add up the last three sides of X
There is a point E on the side of the square ABCD, and the bisector of the angle DAE intersects CD at F
Let DAF be angle 1, FAE be 2, EAB be 3, bag be 41 = 2 (angle bisector), and 1 + 3 = angle DFA (internal error). Because triangle ADF is equal to ABG, 2 = 4, angle DFA = AGB, side DF = BG, 3 + 4 = 3 + 1 = angle DFA = AGB, triangle age is isosceles triangle, side AE = be +
There is a group of numbers: 1, 2, 5, 10, 17, 26. Please observe the structural order of this group of numbers and write the eighth number ()
2 is more than 1, 5 is more than 2, 3 is more than 10, 5 is more than 5, 17 is more than 10, 7 is more than 26, 26 is more than 17, 9. The seventh number should be 11 more than 26, that is 37, and the eighth number 13 more than 37, that is 50
So the eighth number is 50
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