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.
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10. A sound wave's amplitude can be modeled by the function y = −7 sin ((x-1) + 4). Within the interval 0 < x < 12, when does the function have an amplitude
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9.522 seconds
4.199 seconds
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Jamal wants to save $48,000 for a down payment on a home. How much will he need to invest in an
account with 11.8% APR, compounding daily, in order to reach his goal in 10 years? Round to the
nearest dollar.
r
nt
Use the compound interest formula, A (t) = P(1 + 1)".
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b. What if the interest were compounding monthly? $
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
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