1. Under some conditions, proper domestic monetary policy may be at odds with the goal of correcting a trade imbalance because: Multiple Choice a. changes in the domestic interest rate cause changes in domestic investment spending. b. the domestic interest rate varies inversely with the value of the dollar. c. changes in the interest rate cause changes in domestic saving. d. changes in the domestic interest rate tend to cause changes in the international value of the dollar. 2. Which of the following is correct? Multiple Choice a. The transactions demand for money is downward sloping because the opportunity cost of holding money varies inversely with the interest rate. b. The asset demand for money is downward sloping because the opportunity cost of holding money increases as the interest rate rises. c. The asset demand for money is downward sloping because bond prices and the interest rate are directly related. d. The asset demand for money is downward sloping because the opportunity cost of holding money declines as the interest rate rises..

1. 1) (6 points) In this exercise, you will create the three types of elementary matrices, analyze their
properties and perform elementary row-operations on matrices using elementary matrices. (a)
(Creating the elementary matrices) Write three functions in python: defE1(n,c,i,j) : defE2(n,i,j) : def
E3(n,c,i) : that creates the three elementary matrices E1,E2 and E3. How to define the above
functions? (i) Start with the identity matrix eye (n). (ii) To define E1(n,c,i,j), replace (row j ) of eye (
n) by (row j)+c.(row i ). (iii) To define E2(n,i,j), interchange rows i and j of eye (n). (iv) To define E3
(n,c,i), multiply row i of eye (n) by c. (b) (The elementary row operations) After you have
successfully completed (a), use the elementary matrices E1,E2 and E3 (equivalently, use the
functions you created in (a)) to obtain the three row operations (replacement, interchange and
scaling) on a matrix A. For this, you have to create three functions below: def replace-row (A,c,i,j) :
def switch-rows (A,i,j) : def scale-row (A,c,i) : What are these functions doing? replace-row (A,c,i,j)
adds c times row j to row i in A. switch-rows (A,i,j) switches rows i and j in matrix A. scale-row (A,c,
i) multiplies row i by c in matrix A. How to define the above functions? (I) Use the elementary
matrices E1,E2 and E3 you created above. (II) To define replace-row (A,c,i,j), you just multiply E1(
n,c,i,j) by A. (III) To define switch-rows (A,i,j), you just multiply E2(n,i,j) by A. (IV) To define scale-
row (A,c,i), you just multiply E3(n,c,i) by A.( 2 points) In this exercise, you will use the functions
you created in Exercise 1(b) to obtain the row reduced echelon form of a given matrix. (a) Work
with the following matrix: A=10020203021220353011 Use the functions you created in Exercise
1(b) (they are elementary row operations) on matrix A above to obtain the reduced echelon form of
A. (b) Note that every time you apply elementary row operations on A, you get intermediate
matrices. Output all intermediate matrices until you obtain the reduced echelon form of A. (2
points) Use Exercise 1(b) to determine if the following set of vectors is linearly independent. 120,2
41,361 Show all your outputs/steps.