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Let α be n-dimensional column vector and E be n-order identity matrix. It is proved that A=E-2 T/( Tα) is an orthogonal matrix.
Prove: A^T=E^T-2( T)^T/( TT-2( T)^T/( Tα)=E-2 T/( Tα), AA^T=[ E-2 T/( Tα)][ E-2 T/( Tα)]=E-2 T/( Tα)-2 T/( Tα)+4 T T T/( Tα)^2=E-...
How to prove the linear correlation of n+1 dimensional n dimensional vectors?
The necessary and sufficient conditions for linear correlation of vector groups α1,α2,...,αs are
The homogeneous linear equations (α1,α2,...,αs) x=0 have nonzero solutions.
For n+1 dimensional n-dimensional vectors, because r (α1,α2,..,αn+1)
I don't understand that n+1 n-dimensional vectors must be linearly related, and the linear correlation is linearly independent and is connected with the solution of the system of equations.
If the number of unknowns is more than n (the number of unknowns is more than the number of equations), there must be an infinite number of solutions If the number of unknowns is equal to n (the number of unknowns is n equations), then...
ON THE N+1 N-DIMENSIONAL VECTORS For example, must a =(1,1,1) b =(1,2,3) c =(4,5,6) d =(7,8,9) abcd be correlated?
Is...
It can be proved by counter-evidence
Yes...
It can be proved by reverse proof
Known vector A =(2,3), B=(-1,2) if m A+n B and A-2 B collinear, then m N equals () A.-1 2 B.1 2 C.-2 D.2
M
A+n
B=(2m-n,3m+2n),
A-2
B=(4,-1), m
A+n
B and
A-2
B collinear,
(2M-n)(-1)-4(3m+2n)=0,-14m=7n, then m
N=-1
2,
Therefore, A.
Vector a=(1,2), b=(-2,3), if ma-nb is collinear with a+2b,(where m, n are R and n is not equal to 0), then m/n is
Ma-nb=m (1,2)-n (-2,3)=(m+2n,2m-3n),
A+2b=(1,2)+2(-2,3)=(-3,8),
Ma-nb is collinear with a+2b
8(M+2n)+3(2m-3n)=0
M/n=-1/2
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