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Arte-miy333 [17]
3 years ago
10

How do I find x? Do I find the hypotenuse of 15 and 18, then with that answer minus it by 22^2 in a root?

Mathematics
1 answer:
pogonyaev3 years ago
7 0
8+x= \sqrt{22^2-15^2} => 8+x = 15 => x = 15-8=7
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Let T:V→W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W.
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Answer:

The range of T is a subspace of W.

Step-by-step explanation:

we have T:V→W

This is a linear transformation from V to W

we are required to prove that the range of T is a subspace of W

0 is a vector in range , u and v are two vectors in range T

T = T(V) = {T(v)║v∈V}

{w∈W≡v∈V such that T(w) = V}

T(0) = T(0ⁿ)

0 is  Zero in V

0ⁿ  is zero vector in W

T(V) is not an empty subset of W

w₁, w₂   ∈ T(v)

(v₁, v₂ ∈V)

from here we have that

T(v₁) = w₁

T(v₂) = w₂

t(v₁) + t(v₂) = w₁+w₂

v₁,v₂∈V

v₁+v₂∈V

with a scalar ∝

T(∝v) = ∝T(v)

such that

T(∝v) ∈T(v)

so we have that T(v) is a subspace of W. The range of T is a subspace of W.

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