- #1
PenTrik
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Homework Statement
If V is the subspace spanned by (1,1,1) and (2,1,0), find a matrix A that has V as its row space. Find a matrix B that has V as its nullspace
Homework Equations
Ax = 0 for a nullspace
The Attempt at a Solution
So straight off the bat, I think I can solve the first part. Should be simple enough right? Matrix A that has V as its row space is just the matrix
[[1,1,1]
[2,1,0]]
But how do I find matrix B that has V as its nullspace?
The only thing I can possibly think of its to do what I have done before which is to do the rref
Which I think gives me
[[1,0,-1]
[0,1,2]]
Do I run linear combination on the row space from here?Also, a similar question that I am having problems with is
Find a basis for the space of a 2x3 matrices whose nullspace contains (2,1,1)
I'm not even sure how to approach this question. My gut instinct tells me to run matrix multiplication on this one, such that
[tex]
\begin{pmatrix} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \end{pmatrix} \begin{pmatrix} 2 \\ 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}
[/tex]
This is about as far as my understanding of nullspaces carries me.