Let V be the vector space of all functions from the real field R. into R. Show that the set W = {f: f(7) = 2 + f(1)} is not a subspace of V. An arch is in the from of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola? A beam is sopported at its ends by two supports which are 12 m apart. Since the load concentrated at its center, there is a deflection of 3 cm at the center and the deflected beam is in the shape of a parabola. How far from the center is the deflection 1 cm?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let V be the vector space of all functions from the real field R. into R.
Show that the set
W = {f: f(7) = 2 + f(1)}
is not a subspace of V.
An arch is in the from of a parabola with its axis vertical. The arch is 10 m high and
5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
A beam is sopported at its ends by two supports which are 12 m apart. Since the load is
concentrated at its center, there is a deflection of 3 cm at the center and the deflected
beam is in the shape of a parabola. How far from the center is the deflection 1 cm?
Transcribed Image Text:Let V be the vector space of all functions from the real field R. into R. Show that the set W = {f: f(7) = 2 + f(1)} is not a subspace of V. An arch is in the from of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola? A beam is sopported at its ends by two supports which are 12 m apart. Since the load is concentrated at its center, there is a deflection of 3 cm at the center and the deflected beam is in the shape of a parabola. How far from the center is the deflection 1 cm?
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