Question

find the bases for this sets which are the subspaces for which alpha+beta is an element of w.

a) w={(x;y;z)such that x=2z,y=-3z}
b)w={(p;q;r)such that q=p+r}

Answer 1

a basis let's you define any vector in the subspace as a linear combination of the vectors in the basis. For (a), it looks like you can use z as the basis. x= 2z, and y= -3z
(you could use x: z= (1/2)*x, y= (-3/2)*x , or y , for that matter)

Answer 2

ok then,

Answer 3

i'm i gonna assign it to zero then use matrices, according to the definition of bases?

Answer 4

I don't remembering doing this kind of problem, so I'm not much help in deciphering this question.

Answer 5

@mukushla check pls

Answer 6

@myininaya check this pls

Answer 7

remainder are you studying in university of limpopo? because we did the exact same thing a couple of days ago.

Answer 8

definetely but we did'n do this one

Answer 9

we only showed that it subspace we never prove as the bases

Answer 10

@UnkleRhaukus check this pls

Answer 11

yes m also trying to get some stuff online to prove it as a base.

Answer 12

\[W=\left\{ {\left.(x,y,z)\right| x=2z,\quad y=-3z}\right\} \]

Answer 13

\[(x,y,z)\quad\rightarrow\quad(2z,-3z,z)\]

Answer 14

then from here am i gonna let \[\alpha=(2z_1,-3z_1,z_1) ; \beta=(2z_2,-3z_2,z_2)\] ?

Answer 15

yeah

Answer 16

finding the linear combination
let a,b be the element R

then;



i'm not sure about this step