For Problems 34 − 35 , determine span { v 1 , v 2 } for the given vectors in ℝ 3 , and describe it geometrically. v 1 = ( 1 , 2 , − 1 ) , v 2 = ( − 2 , − 4 , 2 ) .
For Problems 34 − 35 , determine span { v 1 , v 2 } for the given vectors in ℝ 3 , and describe it geometrically. v 1 = ( 1 , 2 , − 1 ) , v 2 = ( − 2 , − 4 , 2 ) .
Solution Summary: The author explains how to determine the spanleftv_1, and describe it geometrically. If every set of vectors in a vector space V can be written as
For Problems
34
−
35
, determine span
{
v
1
,
v
2
}
for the given vectors in
ℝ
3
, and describe it geometrically.
v
1
=
(
1
,
2
,
−
1
)
,
v
2
=
(
−
2
,
−
4
,
2
)
.
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.
Suppose ū = (0, 1) and 7 = (−3,−1) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the
parallelogram are
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer
should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3.
(-4,-8, 6) =
-3a1+a2+2a3
b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form .
[(-4,-8,6)] =
Suppose that the vectors [1, –3, 1] and [2, 4, – 1] form the sides of a
parallelogram. Find the lengths of the two diagonals of the parallelogram. Round off your
answer to exactly 3 decimal places and separate your answers with a comma, do not
leave a space in between.
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