vectorial subspace

[dim wind]

is this a subspace?

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[vocal prawn]

what's your attempt on your question?
what do you know about subspace?

[dim wind]

i know whats a subspace and the conditions for it to be a subspace

but thats the only information i got about the exercise

[fierce wing]

Try applying them to check

[dim wind]

yeah but thats where im stuck

because idk how to apply them ig??

if x = 0, i have a vector U = (0, y1, z1) and V (0, y2,z2)

[fierce wing]

For the 0 vector just put x ,y,z = 0 and check of the conditon x=0 is correct

[dim wind]

U + V = (0, y1+y2, z1+z2) and then what

[fierce wing]

X in u+v = 0 so u can say its closed under addition

C(x,y,z : x=0)

For multiplication

[dim wind]

its still closed

so its a subspace then?

[hollow jewel]

yes, scaling (0,y,z) by any scalar leaves the 1st component 0

[fierce wing]

Yes

[dim wind]

ok

thanks!

+close