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. 34. T ( x → ) = x → − 2 ( v → 3 ⋅ x → ) v → 3
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. 34. T ( x → ) = x → − 2 ( v → 3 ⋅ x → ) v → 3
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.
34.
T
(
x
→
)
=
x
→
−
2
(
v
→
3
⋅
x
→
)
v
→
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.
A research study in the year 2009 found that there were 2760 coyotes
in a given region. The coyote population declined at a rate of 5.8%
each year.
How many fewer coyotes were there in 2024 than in 2015?
Explain in at least one sentence how you solved the problem. Show
your work. Round your answer to the nearest whole number.
Answer the following questions related to the following matrix
A =
3
³).
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY