# orthognal

1. ### Basis for orthognal vector

In R3 let S=span((1,2,4)^T) What is a basis for S^(perpendicular)? I know that 0=x*y=1y1+2y2+4y3 and that y2 and y3 are free variables so y1=-2y2-4y3 i have then tried to solve for each of the vectors this way but it is not correct. Please help? Thank You, Diggidy
2. ### Orthogonal Vectors

Let u = <-1, 1, 2> and v = <2, -1, -1>. Find all unit vectors orthogonal to both u and v. I know that one can use cross products to find a vector orthgonal to both u and v and scale it down to be a unit vector. But the question says to find all the unit vectors and I don't know how to go about...
3. ### Find the ceneter of the curve in 3D made by 4-points

A(Ax,Ay,Az) B(Bx,By,Bz) C(Cx,Cy,Cz) D(Dx,Dy,Dz) EXAPMLE: Points X Y Z a -2.00 0.00 -1.00 b -2.00 0.00 -1.59 c -1.59 0.00 -2.00 d -1.00 0.00 -2.00 The Answer is supposed to be ? Center: X:-1.0 Y:0.0 Z:-1.0 What I am trying to solve is to find the...
4. ### Symmetric Matrices and orthognal

Symmetric Matrices and orthogonal Hi, I want to show that if A(nxn) is symmetric then it is orthogonally equivalent to a symmetric matrix wit equal elements in the diagonal.For example for 2x2 if A=[a b;b c] there exist a Q O(2) (Q is orthogonal matrix)such thet : Q 'AQ=[d e;e d]...
5. ### Orthognal matrices are compact

HI, How can I prove the set of compact matrices are compact