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) ![T(A+B) = (A+B)^T = A^T + B^T = T(A) + T(B)](https://tex.z-dn.net/?f=T%28A%2BB%29%20%3D%20%28A%2BB%29%5ET%20%3D%20A%5ET%20%2B%20B%5ET%20%3D%20T%28A%29%20%2B%20T%28B%29)
And we can express like this ![T(A+B) =T(A) + T(B)](https://tex.z-dn.net/?f=%20T%28A%2BB%29%20%3DT%28A%29%20%2B%20T%28B%29)
3) If
and
then we have this:
![T(cA) = (cA)^T = cA^T = cT(A)](https://tex.z-dn.net/?f=%20T%28cA%29%20%3D%20%28cA%29%5ET%20%3D%20cA%5ET%20%3D%20cT%28A%29)
And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.
The slope is the change in y over the change in x.
The first number in the parentheses is the x value, the second number is the y value.
Slope = (0-3) / (4-0)
Slope = -3/4
The y intercept is the y value when x is 0.
The given point (0,3) has x as 0, so the y intercept would be 3
Answers: slope = -3/4, y intercept = 3
Ok now im finna explain it it was 54 dollars and 2 children is the same price as 1 adult ticket so you can just divide 54 by 3 and you well get 18 dollars
Answer:
Alternate exterior: 5 and 4
Corresponding: 6 and 8
Alternate Interior: 2 and 7
Step-by-step explanation:
Alternate exterior means the opposite angle on the exterior. Examples are 5 and 4 or 1 and 8.
Corresponding angles are angles that are congruent but one is on the outside and the other on the inside, they're also on the same line. Examples are 6 and 8, 2 and 4, 3 and 1, 7 and 5, etc.
Alternate interior angles are the same as Alternate exterior angles but on the interior. Examples being 6 and 3 or 2 and 7