Results 1 to 2 of 2

Math Help - d

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    11

    Subspaces

    OOPS I MESSED UP THE TITLE CAN ANY1 TELL ME HOW I CAN CHANGE IT?

    Let  V = R^3, and consider the following subsets of V.

     U_1 = \{ t \begin{pmatrix}<br />
1\\ <br />
0\\ <br />
0\end{pmatrix} : t \in R \}

     U_2 = \{ t \begin{pmatrix}<br />
0\\ <br />
1\\ <br />
0\end{pmatrix} : t \in R \}

     U_3 = \{t \begin{pmatrix}<br />
1\\ <br />
1\\ <br />
1\end{pmatrix} : t \in R \}

     U_4 = \{ \begin{pmatrix}<br />
r\\ <br />
s\\ <br />
0\end{pmatrix} : r,s \in R \}

     U_5 = \{ \begin{pmatrix}<br />
r\\ <br />
s\\ <br />
1\end{pmatrix} : r,s \in R \}

     U_6 = \{ \begin{pmatrix}<br />
r\\ <br />
s\\ <br />
0\end{pmatrix} : r,s,t \in R \text{ and } r+s+t=1 \}

     U_7 = U_1 \cap U_2

     U_8 = U_1 \cup U_2

    a) For each of the 8 sets sat whether it is a subspace, and briefly explain your answer.

    b) For each of the 8 sets, classify it as one of
    i. A line passing through the origin.
    ii. A line not passing through the origin.
    iii. A plane passing through the origin.
    iv. A plane not passing through the origin.
    v. none of the above

    c) What do you conclude about the subspaces of R^3?
    Last edited by I Congruent; October 13th 2008 at 11:25 AM. Reason: Origional title was a mistake
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2008
    Posts
    11
    I am not too confident with my answers and im completely stuck on part b)
    Last edited by I Congruent; October 14th 2008 at 03:28 AM.
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum