Determine if following subsets of R^2 are subspaces of R^2. If the subset is a subspace show that it is closed under vector addition and scalar multiplication. If the subset is not a subspace show why, indicating property that fails.(adsbygoogle = window.adsbygoogle || []).push({});

[tex] 1) W=\{ \left (x_1,0)\left| x_1\in\Re\} \newline [/tex]

[tex] 2) W=\{ \left (x_1,0)\left| x_1 > 0\} \newline[/tex]

[tex]3) W=\{ \left (2c,-3c)\left| c \in\Re\} \newline[/tex]

[tex]4) W=\{ \left (x_1,x_2)\left| x_1 > 0, x_2>0\} \newline [/tex]

Answers:

[tex] 1) (x,0) + (y,0)= (x+y,0) \in W \} \newline [/tex]

[tex] c(x,0) = (c(x),0) \in W \} \newline [/tex]

2) Not subspace since x1 can't be 0

[tex] 3) (2c,-3c) + (x_1,x_2)= (2c+x_1,-3c+x_2) \in W \} \newline [/tex]

[tex] x(2c,-3c) = (2c(x),-3c(x)) \in W \} \newline [/tex]

4) Not a subspace since x1 and x2 can't be 0.

Am I on the right track with this? Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Another vector problem

**Physics Forums | Science Articles, Homework Help, Discussion**