Linear Algebra (Symmetric Matrix)

MoBaT
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A 3x3 symmetric matrix has a null space of dimension one containing the vector (1,1,1). Find the bases and dimensions of the column space, row space, and left null space.

I understand how to get the Dim of Col(A), Row(A), and Nul(A^T) but how do i get the bases with just knowing the dimension of one vector? How should I approach this?
 
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Hey MoBaT.

Can you pick any linearly independent basis?
 
chiro said:
Hey MoBaT.

Can you pick any linearly independent basis?

Dosen't say anything against it. I know what the answer is becuase he gave it to us. It was like:

Dim of Col(A) = 2, dim Row(A) = 2, Dim Nul(A^T) = 1
Basis Row(A) = {[-1 1 0], [-1 - 1]}. Because A is symmetric, Col(A) = Row(A) and Nul(A^T) = Nul(A).

I understand everything after the Basis row(A) but do not understand how he got that Row(A)
 
Found out how to do it. Pretty much fill in the rest of the information with the identity matrix.
 
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