Given x 1 = ( 1 , 1 , 1 ) T and x 2 = ( 3 , − 1 , 4 ) T : (a) Do x 1 and x 2 span ℝ 3 ? Explain. (b) Let x 3 be a third vector in R 3 and set X = ( x 1 , x 2 , x 3 ) . What condition(s) would X have to satisfy in order for x 1 , x 2 , and x 3 to form a basis for ℝ 3 ? (c) Find a third vector x 3 that will extend the set { x 1 , x 2 } to a basis for ℝ 3 .
Given x 1 = ( 1 , 1 , 1 ) T and x 2 = ( 3 , − 1 , 4 ) T : (a) Do x 1 and x 2 span ℝ 3 ? Explain. (b) Let x 3 be a third vector in R 3 and set X = ( x 1 , x 2 , x 3 ) . What condition(s) would X have to satisfy in order for x 1 , x 2 , and x 3 to form a basis for ℝ 3 ? (c) Find a third vector x 3 that will extend the set { x 1 , x 2 } to a basis for ℝ 3 .
Given
x
1
=
(
1
,
1
,
1
)
T
and
x
2
=
(
3
,
−
1
,
4
)
T
: (a) Do
x
1
and
x
2
span
ℝ
3
? Explain. (b) Let
x
3
be a third vector in
R
3
and set
X
=
(
x
1
,
x
2
,
x
3
)
. What condition(s) would X have to satisfy in order for
x
1
,
x
2
, and
x
3
to form a basis for
ℝ
3
? (c) Find a third vector
x
3
that will extend the set
{
x
1
,
x
2
}
to a basis for
ℝ
3
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
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