Let x 1 = ( 2 1 3 ) , x 2 = ( 3 − 1 4 ) , x 3 = ( 2 6 4 ) (a) Show that x 1 , x 2 , and x 3 are linearly dependent. (b) Show that x 1 and x 2 are linearly independent. (c) What is the dimension of Span ( x 1 , x 2 , x 3 ) ? (d) Give a geometric description ofSpan ( x 1 , x 2 , x 3 ) .
Let x 1 = ( 2 1 3 ) , x 2 = ( 3 − 1 4 ) , x 3 = ( 2 6 4 ) (a) Show that x 1 , x 2 , and x 3 are linearly dependent. (b) Show that x 1 and x 2 are linearly independent. (c) What is the dimension of Span ( x 1 , x 2 , x 3 ) ? (d) Give a geometric description ofSpan ( x 1 , x 2 , x 3 ) .
Solution Summary: The author explains that given vectors are linearly dependent because x_1 is linear combination of
Let
x
1
=
(
2
1
3
)
,
x
2
=
(
3
−
1
4
)
,
x
3
=
(
2
6
4
)
(a) Show that
x
1
,
x
2
, and
x
3
are linearly dependent. (b) Show that
x
1
and
x
2
are linearly independent. (c) What is the dimension of Span
(
x
1
,
x
2
,
x
3
)
? (d) Give a geometric description ofSpan
(
x
1
,
x
2
,
x
3
)
.
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