![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given that the standard deviation of a group of data X1 x2 X3 is 2, then the standard deviation of data 2x1 + 3,2x2 + 3,2x3 + 3D is fast!
Variance of the first set of data var (x) = 2 ^ 2 = 4
The variance of the second group of data var (2x + 3) = 2 ^ 2 * var (x) = 16, standard deviation = root 16 = 4
Formula var (AX + b) = a ^ 2 * var (x)
It is known that the n-dimensional vectors A1, A2, A3, A4, A5 are linearly independent and a is an invertible matrix of order n. It is proved that Aa1, aa2, aa3, AA4, aa5 are linear
Because (Aa1, aa2, aa3, AA4, aa5) = a (A1, A2, A3, A4, A5)
And a is reversible
So r (Aa1, aa2, aa3, AA4, aa5) = R [a (A1, A2, A3, A4, A5)] = R (A1, A2, A3, A4, A5) = 5
So Aa1, aa2, aa3, AA4, aa5 are linearly independent
Let a and B be n-dimensional column vectors, then the rank of n-order matrix C = AB ^ t is R (a) =, why not equal to N, and the answer is 0 or 1
Let a = (A1, A2,. An) ^ t, B = (B1, B2,. BN) ^ t
Then AB ^ t = A1B1, A1B2, a1b3. A1bn
a2b1 a2b2 a2b3 .a2bn
..
anb1 anb2 anb3 .anbn
Note any 2 * 2 submatrix AiBj aibk
asbj asbk
Its determinant is 0, so any k (greater than or equal to 2) level subexpression is equal to 0
So the rank of AB ^ t
Let a be your cubic matrix, A1 and A2 be the eigenvectors of a which belong to the eigenvalues - 1 and 1 respectively. Let the vector A3 satisfy aa3 = A2 + a3, let P = (A1, A2, A3), and find p-1ap
Known by
AP = A(a1,a2,a3)
= (Aa1,Aa2,Aa3)
= (-a1,a2,a2+a3)
= (a1,a2,a3) B
B=
-1 0 0
0 1 1
0 0 1
So AP = PB
So p ^ - 1AP = B=
-1 0 0
0 1 1
0 0 1
RELATED INFORMATIONS
- 1. Let a be a square matrix of your order, A1 and A2 be the eigenvectors of a belonging to the eigenvalues - 1 and 1 respectively, and the vector A3 satisfy that aa3 = A2 + a3, let P = (A1, A2, A3), and find p-1ap
- 2. 4. When we ask what value a takes, the following vector groups are linearly correlated? A1 = (a, 1,1), A2 = (1, a, - 1) t, A3 = (1, - 1, a) t
- 3. In R4, find two linearly independent vectors A3 and A4 orthogonal to A1 = (1,0,1,0) t and A2 = (1,0,1,1) t, and find the standard orthogonal basis The answer unites A1 and A2. The orthonormal basis has four vectors, but the inner product of A1 and A2 is not zero. Shouldn't the four vectors be orthogonal to each other and the inner product be zero?
- 4. Given vector group A1 = (111), A2 = (101) A3 = (0320) A4 = (- 1101), find the rank of vector group A4 = (- 1 10 - 1) wrong title
- 5. Let A1 = (2,1,3) A2 = (1,2,0), A3 = (- 1,1,0) prove that the vector group a1a2a3 is independent
- 6. Let vector group A1, A2, A3 As is linearly independent (s > 2), try to prove that the following vector groups are vector independent: A1, a1 + A2, a1 + A2 + a3 a1+a2+…… as
- 7. Let a be a square matrix of order 3, | a | = - 4, let AI be the i-th column vector of a, then a = (A1, A2, A3), then the determinant | A3 + 3A1, A2, 4A1 | =
- 8. Let A1, A2, A3 and A4 be four-dimensional vectors, and a = (A1, A2, A3 and A4) have known the general solution x = K (1,0,1,0) ^ t, and find the solution of A1, A2, A3 and A4 of vector group The answer is R (a) = 3. How did this come about? Finding the maximal independent group of A1, A2, A3, A4 of vector group
- 9. Given a vector group A1 = (1. - 1,2,4), A2 = (0.3.1.2) A3 = (3,0,7,14) A4 = (1. - 1,2,0) A5 = (2,1,5,6), then the rank of this vector group is
- 10. If the sequence {an} satisfies A2 + A4 = 20, A3 + A5 = 40, then the common ratio q = () A. 12B. -12C. 2D. -2
- 11. If the variance of x1, X2, X3 is 2, then the variance of data 2x1-1, 2x2-1, 2x3-1 is ()
- 12. Calculation formula of standard deviation
- 13. If the average of x1, X2, X3, X4 is 5, then the average of 5x1 + 1, 5x2 + 1, 5x3 + 1, 5X4 + 1 is 5______ ．
- 14. Let f (x) = 4 ^ 2-2 ^ (x + 1), then f ^ - 1 (0) = (inverse function problem)
- 15. If the original function increases monotonically in the interval [- A, a], then there must be an inverse function and the inverse function also increases monotonically; but if a function has an inverse function, this function is different This function is not necessarily monotonic,
- 16. If FX is the inverse function of the function GX = (1 / 2) 2, then the monotone increasing interval of F (4-x2)
- 17. Inverse function of function y = (e ^ x) - 1 [f ^ (- 1)] (x)= Such as the title
- 18. F (x) = e ^ x + e ^ (- x), the calculation process of inverse function
- 19. Is the X in f ^ - 1 (x) in the inverse function the X of the original function or the X in the inverse function, that is, the Y in the original function?
- 20. The inverse function of F (x) = a ^ x (a > 0 and a ≠ 1), y = ^ - 1 (x), f ^ - 1 (2) + f ^ - 1 (5) = 1 Reply as soon as possible What is the concrete expression of the inverse function of a ^ x?