Let v 1 = ( 0 , 6 , 3 ) , v 2 = ( 3 , 0 , 3 ) , and v 3 = ( 6 , − 3 , 0 ) . Show that { v 1 , v 2 , v 3 } is a basis for ℝ 3 . [ Hint: You need not show that the set is both linearly independent and a spanning set for ℝ 3 . Use a theorem from this section to shorten your work.]
Let v 1 = ( 0 , 6 , 3 ) , v 2 = ( 3 , 0 , 3 ) , and v 3 = ( 6 , − 3 , 0 ) . Show that { v 1 , v 2 , v 3 } is a basis for ℝ 3 . [ Hint: You need not show that the set is both linearly independent and a spanning set for ℝ 3 . Use a theorem from this section to shorten your work.]
Solution Summary: The author explains that a set of vectors leftv_1,
Let
v
1
=
(
0
,
6
,
3
)
,
v
2
=
(
3
,
0
,
3
)
, and
v
3
=
(
6
,
−
3
,
0
)
. Show that
{
v
1
,
v
2
,
v
3
}
is a basis for
ℝ
3
. [Hint: You need not show that the set is both linearly independent and a spanning set for
ℝ
3
. Use a theorem from this section to shorten your work.]
College Algebra with Modeling & Visualization (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.