In R 3 , a line through the origin is the set of all points in R 3 whose coordinates satisfy x 1 = a t , x 2 = b t , and x 3 = c t where t is a variable and a , b , and c are not all zero. Show that a line through the origin is a subspace of R 3 .
In R 3 , a line through the origin is the set of all points in R 3 whose coordinates satisfy x 1 = a t , x 2 = b t , and x 3 = c t where t is a variable and a , b , and c are not all zero. Show that a line through the origin is a subspace of R 3 .
In
R
3
, a line through the origin is the set of all points in
R
3
whose coordinates satisfy
x
1
=
a
t
,
x
2
=
b
t
, and
x
3
=
c
t
where t is a variable and a, b, and c are not all zero. Show that a line through the origin is a subspace of
R
3
.
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