Answer:
See picture and explanation below.
Step-by-step explanation:
With this information, the matrix A that you can find is the transformation matrix of T. The matrix A is useful because T(x)=Av for all v in the domain of T.
A is defined as ![T=([T(v_1)] [T(v_2] [T(v_3)])\text{ where }[T(v_i)]](https://tex.z-dn.net/?f=T%3D%28%5BT%28v_1%29%5D%20%5BT%28v_2%5D%20%5BT%28v_3%29%5D%29%5Ctext%7B%20where%20%7D%5BT%28v_i%29%5D)
denotes the vector of coordinates of 
respect to the basis 
(we can apply this definition because 
forms a basis for the domain of T).
The vector of coordinates can be computed in the following way: if 
then ![[T(v_i)]=(a_1,a_2,a_3)^t](https://tex.z-dn.net/?f=%5BT%28v_i%29%5D%3D%28a_1%2Ca_2%2Ca_3%29%5Et)
.
Note that we have all the required information: 
then ![[T(v_1)]=(0,1,0)^t](https://tex.z-dn.net/?f=%5BT%28v_1%29%5D%3D%280%2C1%2C0%29%5Et)
hence ![[T(v_2)]=[T(v_3)]=(1,0,0)^t](https://tex.z-dn.net/?f=%5BT%28v_2%29%5D%3D%5BT%28v_3%29%5D%3D%281%2C0%2C0%29%5Et)
The matrix A is on the picture attached, with the multiplication A(1,1,1).
Finally, to obtain the output required at the end, use the properties of a linear transformation and the outputs given:
In this last case, we can either use the linearity of T or multiply by A.
Answer:
6
come to z o o m
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<h3>
Answer: -13</h3>
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Explanation:
g(-3) = 2 means x = -3 and y = 2 pair up together to form the point (-3,2)
g(1) = -4 means we have the point (1,-4)
Find the slope of the line through the two points (-3,2) and (1,-4)
m = (y2-y1)/(x2-x1)
m = (-4-2)/(1-(-3))
m = (-4-2)/(1+3)
m = -6/4
m = -3/2
m = -1.5
The general slope intercept form y = mx+b turns into y = -1.5x+b after replacing m with -1.5
Plug in (x,y) = (-3,2) which is one of the points mentioned earlier and we end up with this new equation: 2 = -1.5*(-3) + b
Let's solve for b
2 = -1.5*(-3)+b
2 = 4.5 + b
2-4.5 = 4.5+b-4.5 .... subtract 4.5 from both sides
-2.5 = b
b = -2.5
Therefore, y = mx+b becomes y = -1.5x-2.5 meaning the g(x) function is g(x) = -1.5x-2.5
The last step is to plug in x = 7 and compute
g(x) = -1.5*x - 2.5
g(7) = -1.5*7 - 2.5
g(7) = -10.5 - 2.5
g(7) = -13
