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A matrix is obtained by multiplying a column vector by a row vector. How to get the original column vector and row vector from the result matrix?
If the result matrix is 0, then both vectors are 0 vectors
If the result matrix is not 0:
Find a nonzero line, and the rest must be multiples of this line
This nonzero row is used as the row vector
The multiple forms the column vector
Can a ^ 2-e = (A-E) (a + e) be equal to (a + e) (A-E) in matrix and its operation in Engineering Mathematics and linear algebra?
I hope I can explain more
Yes
This is because a and E are interchangeable
(A+E)(A-E) = A^2-AE+EA-E^2 = A^2-A+A-E = A^2-E.
Similarly, there is another equation
3x+6=18 2x-7.5=8.5 16+8x=40 4x-3X9=29
3X+6=18 3X=18-6 3X=12 X=12/3 X=4 2X-7.5=8.5 2X=7.5+8.5 2X=16 X=16/2 X=8 16+8X=40 8X=40-16 8X=24 X=24/8 X=3 4X-3*9=29 4X-27=29 4X=29+27 4X=56 X=56/4 X=14
Derivation: y = xsinx + 1 / 2 * cosx, what is the derivative when x = pi / 4?
y'=x'*sinx+x*(sinx)'+1/2*(-sinx)
=sinx+x*cosx-1/2*sinx
=x*cosx+1/2*sinx
x=π/4
So y '= π / 4 * cos π / 4 + 1 / 2 * sin π / 4
=(π√2+2√2)/8
Kindergarten math problem everyone to help!
The title is:
A person puts a table tennis ball into two kinds of boxes, 12 in each big box and 5 in each small box. If the number of table tennis balls is 103, how many in each box?
If there are x large boxes and Y small boxes, then there are 12x + 5Y = 103. It can be concluded that only when x = 4 and y = 11 can the condition be satisfied. Four boxes with 12 boxes and 11 boxes with 5 boxes are used. The specific algorithm is that one kind of box is x, and the other kind of box is y. 12x + 5Y = 103 ∵ 103 is odd ∵ y is odd, and the end of 12x is 8 within 100
On the system of equations ax + by = 5 2x-3y = 4. Ax by = 8. X + by = 7 of XY to find a-b
We can get ax + by = 5, ax by = 8, ax = 13 / 2, by = - 3 / 2
Because x + by = 7, x = 17 / 2
So a = 17 / 13,
And because 2x-3y = 4, y = 13 / 3
So B = - 9 / 26
a-b=17/13-(-9/26)=43/26
Select nine numbers from the ten numbers of 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to form a two digit number, a three digit number and a four digit number, so that the sum of the three numbers equals 2010, then the unselected number is______ ．
The sum of all the digits in the addend and the sum of all the digits in the sum should be an integral multiple of 9. Because the sum of all the digits in 2010 is: 2 + 0 + 1 + 0 = 3, 0 + 1 + 2 + +9 = (1 + 9) △ 2 = 45; 45 is a multiple of 9, 3 plus 6 is a multiple of 9, so 6 should be removed from it
It is known that the intersection of a straight line y = KX + B (K ≠ 0) and a hyperbola y = k ^ 2 / X is at points m (m, - 1), n (n, 2)
Given that the intersection of straight line y = KX + B (K ≠ 0) and hyperbola y = k ^ 2 / X is at points m (m, - 1), n (n, 2), then the inequality (X-B) / k > k ^ 2 / X
(it's OK to have an idea. If there is a process, it's best!)
Then the solution set of inequality (X-B) / k > k ^ 2 / X is__________
Substituting the coordinates of M and n into two function expressions, four equations can be obtained: km + B = - 1, kn + B = 2, K ^ 2 / M = - 1, K ^ 2 / N = 2, (1) - (2) get k (m-n) = - 3, (3) - (4) get k ^ 2 (n-m) / (MN) = - 3, so K / (MN) = - 1, that is, k = - Mn, (3) * (4) get k ^ 4 / (MN) = - 2
Only one minus sign, two plus signs and one bracket can be added to make 1,2,3,4,5,6,7,8,9 column into one formula. The result is equal to 100. How to column?
123-（45+67）+89=100
Quadratic function in quadratic equation of one variable
If the square of parabola y = - x + 2 (M + 1) x + m + 3 intersects with X axis at two points a and B, and OA ratio ob = 3:1, then the value of M is ()
Let y = 0, then x = (M + 1) ± √ [(M + 1) ^ 2 + m + 3] + means on the right side of Y-axis and - means on the left side of y-axis
According to OA ratio ob = 3:1, it can be concluded that:
(1) Point a is on the right side of the y-axis
(m+1)＋√【（m+1)^2+m+3】＝－3『（m+1)－√【（m+1)^2+m+3】』
We can get 2 (M + 1) = √ [(M + 1) ^ 2 + m + 3]
M = 0 or M = - 5 / 3
(2) Point a is on the left side of the y-axis
-『（m+1)－√【（m+1)^2+m+3】』=3{(m+1)＋√【（m+1)^2+m+3】}
The reduction is - 2 (M + 1) = √ [(M + 1) ^ 2 + m + 3]
So we can get
M = - 5 / 3, M = 0
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