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Math For Social Sciences. Practice Exam

Use the elimination method to solve each of the following systems:
- Answer: x=-z, y=-1+2z, z=z.
- Answer: x=3 and y=4.
Let , , and .
- Give the dimensions of each matrix, and identify any square, column, or row matrices.
  
  Answer: A is a matrix. B is a column matrix. C is a row matrix. D is a square matrix.
- Find the following if possible:
  - 2AD.
    
    Answer:
  - BC.
    
    Answer:
  - CA.
    
    Answer:
Use the Gauss Jordan method to solve the following system:

Answer: x=-1, y=1, and z=-2.
Use the method of matrix inverses to solve the following system:

Answer: x=1 and y=-1.
A 45-year-old man puts $1,000 in a retirement account at the beginning of each quarter until he reaches the age of 60 and makes no further deposits. If the account pays 11% interest compounded quarterly, how much will be in the account when the man reaches age 60?

Answer: The money in the account will be approximately $148,809.
A speculator agrees to pay $15,999 for a parcel of land; this amount, with interest, will be paid over 4 yr, with semiannual payments, at an interest rate of 10% compounded semiannually. Find the amount of each payment.

Answer: Each payment will be approximately $2475.39.