Select one: a. You get a function that maps each vector x to two times itself 2x b. You get a function that maps each vector x to negative two times itself −2x c. You get a function that maps each vector x to its opposite −x d. You get a function that maps each vector x to itself x Which of the following matrices is the inverse matrix of A=( 1
0
​
2
1
​
) ? Select one: a. A −1
=( 1
0
​
2
1
​
) b. A −1
=( 1
0
​
− 2
1
​
1
​
) c. A −1
=( 1
0
​
2
1
​
1
​
) d. A −1
=( 1
0
​
−2
1
​
) What is the integrating factor for the first-order linear nonhomogeneous ODE dt
dy
​
=t 2
y+t 3
? Hint: write the differential equation in a different form first. Select one: a. μ(t)=e t t
/4
b. μ(t)=e t t 3
/3
c. μ(t)=e −t 3
/3
d. μ(t)=e −t t
/4
(2) Find a general solution of the first-order linear nonhomogeneous ODE dt
dy
​
−−3y+2sin(4t). You may use any method you like, though you will benefit from working on doing it by Mathematica. The Method of Undetermined Coefficients is probably easier to use than the Method of Integrating Factors here, though you might want to try it both ways. Select one: a. y=Ce −3t
− 25
8
​
cos(4t)+ 25
6
​
sin(4t) b. y=Ce −3t
+ 25
8
​
cos(4t)− 25
6
​
sin(4t) c. y=Ce 3t
+ 25
8
​
cos(4t)− 25
6
​
sin(4t) d. y=Ce 3t
− 25
8
​
cos(4t)+ 25
6
​
sin(4t) What fact about derivatives makes it so that the Method of Integrating Factors works? Select one: a. The Quotient Rule b. The Product Rule c. The Inverse Function Derivative Rule d. The Chain Rule