Why is the rank of n-dimensional unit column vector 1?

Matrix of n-dimensional unit column vector belonging to NX1
Rank of matrix = row rank = column rank
The rank of the column is 1, so the rank of the matrix is 1

When an n-dimensional vector is added to a group of n-dimensional vectors with rank n, the rank of the vector group is equal to?

Let a be a matrix of order n, α 1, α 2 and α 3 be n-dimensional nonzero vectors. If a α I = I α I (I = 1,2,3), it is proved that α 1, α 2 and α 3 are linearly independent

α 1, α 2 and α 3 are the eigenvectors corresponding to the eigenvalues 1, 2 and 3 of a respectively, so they are linearly independent

a. B is a three-dimensional column vector, matrix A = bat (b times (transpose of a)), what is the rank of matrix A? Why? If it is extended to n-dimension?

The rank of matrix A is less than or equal to 1
Because R (a) = R (BA ^ t)

RELATED INFORMATIONS

1. Let a and B be n-dimensional nonzero column vectors, and a = 2e (n-dimensional) - ABT (transpose vector of B) If the square of a = a + 2E, what is the transpose vector of a multiplied by B
2. Let α be an n-dimensional nonzero column vector and E be an n-order identity matrix. It is proved that a = e - (transpose of 2 / α multiplied by α) transpose of α α is an orthogonal matrix
3. Let p be an orthogonal matrix of order n and X be a column vector of n-dimensional unit length, then |||||= ()? What do two verticals mean?
4. 5. The necessary and sufficient condition for a group of n-dimensional vectors to be linearly independent is (). There exists a group of numbers which are not all zero, such that; 5. The necessary and sufficient conditions for the linear independence of n-dimensional vector group are as follows: (1) there exists a group of numbers which are not all zero, so that any two vectors in; (2) there exists a vector in; (3) it cannot be expressed linearly by the other vectors; (4) there is a vector in; (4) there is a vector in; (4) there is a vector in; (4) there is a vector in; (4) there is a vector in; (4) there is a vector in; (4) there is a vector in; (4)
5. In higher algebra, let a be an n-dimensional vector space, then what is the dimension of the vector space composed of all linear transformations on a?
6. If two sets of data x1, X2 , xn and Y1, Y2 The average number of YN is x, y respectively. Find a group of new data: ax1 + by1, AX2 + BY2 The average of axn + byn
7. Let a B be a matrix of order n and a B ab-i be invertible. It is proved that a - (the inverse of B) is invertible
8. Linear algebra A = (1, - 1,1) B = 1 21 10 2 2 21 100 and Ax = B for matrix X Linear algebra A = (1, - 1,1) B = 1,2 1 1 0 2 2 2 1 1 0 0 And Ax = B for matrix X
9. It is proved that R (AB) = R (a) if and only if matrix B is invertible How to prove the necessity?
10. Given the set M = {(x, y) | y ^ 2 = 2x}, n = {(x, y) | (x-a) ^ 2 + y ^ 2 = 9}, the necessary and sufficient conditions for finding m intersection n to be an empty set are given
11. On whether n + 1 n-dimensional vectors are linearly related For example, is a = (1,1,1) B = (1,2,3) C = (4,5,6) d = (7,8,9) ABCD necessarily related?
12. Let a be an n-order square matrix, ξ be an n-dimensional sequence vector, a & # 178; ξ ≠ 0, a & # 179; ξ = 0, and prove that ξ, a ξ, a & # 178; ξ are linearly independent Linear algebra
13. Let X and y be n-dimensional column vectors, and x ^ t * y = 1, matrix A = e + X * y ^ t, then a is an invertible matrix, and find a ^ - 1
14. Let a be a real symmetric matrix and IAI ＜ 0, it is proved that there exists a non-zero n-dimensional column vector x, such that the transpose ax of X
15. Proof: if n-dimensional real vector p is orthogonal to any n-dimensional real vector, then p must be a zero vector
16. Let n-order non pinchable matrix A and n-dimensional column vector α satisfy R {(first row) a α (second row) α t (transpose) 0} = R (a), then the equations AX = α must have infinite solutions Why?
17. In the sequence {an}, it is known that A1 = 0, A2 = 6, and for any positive integer n, there is a (n + 2) = 5A (n + 1) - 6A (n) (1) Let BN = a (n + 1) - 2An, find the general term formula of BN (2) General term formula for an
18. In the sequence {an}, two adjacent terms an and an + 1 are the corresponding quadratic equations Two adjacent terms in sequence {an} an.an +1 is two of the equation x ^ 2 + 3nx + BN = 0. If A1 = 2, try to find the value of B100
19. Determinant calculation | x + A1 A2 A3 an| |x x+a2 a3 …… an| …… |a1 a2 a3 …… x+an|
20. If the sequence A1, A2, A3 and A4 are proportional and A1A2 = - 323, a2a3 = - 24, then q = 0___ ．