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JulsSmile [24]
3 years ago
5

Let T be a linear transformation from a vector space V with dimension 11 onto a vector space W with dimension 7. What is the dim

ension of the nullspace of T?
Physics
1 answer:
erica [24]3 years ago
8 0

Answer:

The dimension of the nullspace of T = 4

Explanation:

The rank/dimension theorem is explains that:

Suppose V and W are vector spaces over F, and T:V → W is linear. If V is finite dimensional, then

nullity(T) + rank(T) = dim(V).

rank(T) = dimension of T = dim(T) = dim(W) = 7

nullity(T) = dimension of the nullspace of T = dim(T) = ?

dim(V) = 11

nullity(T) = dim(V) - dim(T) = 11 - 7

nullity(T) = 4.

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force of friction on the cart is given as

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here we also know the reaction force due to surface

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so we can say reaction force is given as

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now by force balance we will say

F_y + F_n = mg

F_y = mg - F_n

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also we know that

F_f = \mu * F_n

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\mu = 0.39

now minimum force required to set this into motion

F_{min} = \frac{\mu mg}{\sqrt{1 + \mu^2}}

here we know that

mg = F_n = 713 N

F_{min} = \frac{0.39* 713}{\sqrt{1 + 0.39^2}}

F_{min} = 259 N

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Answer:

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Explanation:

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