Numer between 1 and 20 that has exactly 5 factors
1 answer:
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Answer:
True. See the explanation and proof below.
Step-by-step explanation:
For this case we need to remeber the definition of linear transformation.
Let A and B be vector spaces with same scalars. A map defined as T: A >B is called a linear transformation from A to B if satisfy these two conditions:
1) T(x+y) = T(x) + T(y)
2) T(cv) = cT(v)
For all vectors and for all scalars
. And A is called the domain and B the codomain of T.
Proof
For this case the tranformation proposed is t:
Where
For this case we have the following assumption:
1) The transpose of an nxm matrix is an nxm matrix
And the following conditions:
2)
And we can express like this
3) If and
then we have this:
And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.
We are given the following conversion factor:
We are asked to determine how many miles are 140 km. To do that we use the quotient of the conversion factor where the unit we want to convert to is in the numerator and the given unit in the denominator. Since we want to find miles we use the following quotient:
Solving the operations we get: