Let = ( v → 1 , v → 2 , v → 3 ) be any basis of ℝ 3 consisting of perpendicular unit vectors, such that v → 3 = v → 1 × v → 2 . In Exercises 31 through 36, find the matrix B of the given linear transformation T from ℝ 3 to ℝ 3 . Interpret T geometrically. 35. T ( x → ) = x → − 2 ( v → 1 ⋅ x → ) v → 2
Let = ( v → 1 , v → 2 , v → 3 ) be any basis of ℝ 3 consisting of perpendicular unit vectors, such that v → 3 = v → 1 × v → 2 . In Exercises 31 through 36, find the matrix B of the given linear transformation T from ℝ 3 to ℝ 3 . Interpret T geometrically. 35. T ( x → ) = x → − 2 ( v → 1 ⋅ x → ) v → 2
Solution Summary: The author explains how the matrix B can be obtained from column by column method.
Let
=
(
v
→
1
,
v
→
2
,
v
→
3
)
be any basis of
ℝ
3
consisting of perpendicular unit vectors, such that
v
→
3
=
v
→
1
×
v
→
2
. In Exercises 31 through 36, find the matrix B of the given linear transformation T from
ℝ
3
to
ℝ
3
. Interpret T geometrically.
35.
T
(
x
→
)
=
x
→
−
2
(
v
→
1
⋅
x
→
)
v
→
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.
Solve questions by Course Name (Ordinary Differential Equations II 2)
please Solve questions by Course Name( Ordinary Differential Equations II 2)
InThe Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth.
Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth
from which the flash is visible? (Earth’s radius is approximately 4000 miles.)
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