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Answer:
Gina is 12 years old
Step-by-step explanation:
First, we will have to write these statements mathematically and then solve.
Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.
The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)
The next statement "Gina's brother is half Gina's age" can be mathematically written as y = ---------------------------------------(2)
Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)
We can now proceed to solve;
Substitute equation (1) and equation(2) into equation (3)
x + y + z = 42
x + + 2x = 42
Multiply through by 2
2x + x + 4x = 84
7x = 84
Divide both-side of the equation by 7
=
x = 12
Therefore, Gina is 12 years old
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.