showing that two subspaces of $mathbbR^4$ are equal

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I have two subspaces $U,V$ of $mathbbR^4$ where $$U=textspan(u_1,u_2,u_3)\ V=textspan(v_1,v_2)$$ for some vectors $u_1,u_2,u_3, v_1,v_2$. $U$ and $V$ are subspaces of $mathbb R^4$. How can I show that $U=V$?




linear-algebra




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  • To show $Usubseteq V$, prove each $u_iin V$ etc.
    – Lord Shark the Unknown
    Jul 22 at 16:47










  • Show that $dim(U)=dim(V)=dim(Ucup V)$.
    – Michael Hoppe
    Jul 22 at 19:34














up vote
-3
down vote

favorite












I have two subspaces $U,V$ of $mathbbR^4$ where $$U=textspan(u_1,u_2,u_3)\ V=textspan(v_1,v_2)$$ for some vectors $u_1,u_2,u_3, v_1,v_2$. $U$ and $V$ are subspaces of $mathbb R^4$. How can I show that $U=V$?




linear-algebra




share|cite|improve this question





















  • To show $Usubseteq V$, prove each $u_iin V$ etc.
    – Lord Shark the Unknown
    Jul 22 at 16:47










  • Show that $dim(U)=dim(V)=dim(Ucup V)$.
    – Michael Hoppe
    Jul 22 at 19:34












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











I have two subspaces $U,V$ of $mathbbR^4$ where $$U=textspan(u_1,u_2,u_3)\ V=textspan(v_1,v_2)$$ for some vectors $u_1,u_2,u_3, v_1,v_2$. $U$ and $V$ are subspaces of $mathbb R^4$. How can I show that $U=V$?




linear-algebra




share|cite|improve this question













I have two subspaces $U,V$ of $mathbbR^4$ where $$U=textspan(u_1,u_2,u_3)\ V=textspan(v_1,v_2)$$ for some vectors $u_1,u_2,u_3, v_1,v_2$. $U$ and $V$ are subspaces of $mathbb R^4$. How can I show that $U=V$?





linear-algebra





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 22 at 17:06









amWhy

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189k25219431









asked Jul 22 at 16:45









Madhav Madhukar

1




1











  • To show $Usubseteq V$, prove each $u_iin V$ etc.
    – Lord Shark the Unknown
    Jul 22 at 16:47










  • Show that $dim(U)=dim(V)=dim(Ucup V)$.
    – Michael Hoppe
    Jul 22 at 19:34
















  • To show $Usubseteq V$, prove each $u_iin V$ etc.
    – Lord Shark the Unknown
    Jul 22 at 16:47










  • Show that $dim(U)=dim(V)=dim(Ucup V)$.
    – Michael Hoppe
    Jul 22 at 19:34















To show $Usubseteq V$, prove each $u_iin V$ etc.
– Lord Shark the Unknown
Jul 22 at 16:47




To show $Usubseteq V$, prove each $u_iin V$ etc.
– Lord Shark the Unknown
Jul 22 at 16:47












Show that $dim(U)=dim(V)=dim(Ucup V)$.
– Michael Hoppe
Jul 22 at 19:34




Show that $dim(U)=dim(V)=dim(Ucup V)$.
– Michael Hoppe
Jul 22 at 19:34















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