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Math 1090 Section 5 Review3 (5.1-7.2) Matrices 1. 2. 3. 4. 5. 6. 7. Read all directions carefully. This will be graded on completion, but you need to show signicant work toward the solution of the problem. 3 2 3 2 4 2 2 3 2 3 2 4 1 7 6 4 2 6 5 1 2 0 7 7 6 6 6 A = 4 4 9 1 5 B = 64 10 22 45 75 C = 66 3 2 77 D = 4 4 2 5 4 6 1 3 65 5 9 0 5 7 8 1 0 3 2 5 2 3 6 2 7 4 3 2 7 6 E = 4 6 1 1 5 F = 66 3 77 G = 3 2 1 6 10 4 0 5 2 2 1 1 Find the inverse of the matrix 2 3 A if it has one and if it does use the inverse to 2 solve the equation Ax = 4 4 5 0 Jim puts $5000 into a savings account with 6.5% interest compounded 14 times per year. What is the eective rate that Jim is getting on the account? When will the account balance reach $6500? Maximize and minimize Z = 2x2 + y3 subject to x 0, y 0, 4y + 3x 12, 3x + y 6, and y 5 x. Find CDT B and B T DC T if you can preform the multiplication. Find all solutions of 4x + 5y 2z = 7 2x + 3y 6z = 1 2x + 3y = 5 using matrix reduction Find the transpose of all the matrices at the top of the page. Are there any dierent matrices that you can add together at the top of the page? How about with the transpose of a matrix? Find all solutions that satisfy all the following inequalities. 8 < : 4x + y 12 2y + 3x 6 5x 6y 0 8. Ron owes Jim $3000 due in 5 years and he also owes Jane $2000 due in 7 years. He plans to pay o the debt with $x in 3 years, $4x in 8 years, and $1000 in one year. Assuming an account compounded monthly at a rate of 7%, how much is x? 9. 10. 11. 12. 13. Find 2 43 57 + 3 09 43 Bob just bought a new car for $14,500. He found a bank that was willing to nance the car at a rate of 5% compounded monthly. If it will take Bob 6 years to pay o the car what was his monthly payment at the beginning of the month? What was the nance charge? If he decided to instead make payments at the end of the month how much more would the nance charge be? Tom invests $40,000 in a company that guarantees a cash ow of $12,000 in 5 years, $20,000 in 8 years, and $30,000 in 10 years. Assuming an interest rate of 5% compounded quarterly is the investment protable? Joey decides that he will start saving up for retirement. He would like to have $1,000,000 in 30 years. In order to do this he will put away $R at the begining of each month in an account compounded monthly at a rate of 4%. He will also make a payment of $10,000 dollars in 10 years and $20,000 in 20 years. How much is his monthly payment? Find the inverse of matrix E3 if it has one and if it does use the inverse to solve 2 0 the equation Ex = 4 2 5 50 14. Find 3AT 4E T 3A + 4E . 15. Silas makes an investment of $30,000 in a canning company. The company guarantees a cash ow of $5000 in 2 years, $10,000 in 4 years, $20,000 in 8 years. Assuming an interest rate of 3% compounded semi-annually is the investment protable? 16. Find FG and GF . 17. A company decides that in 4 years they are going to need a new air hockey table. The cost of the new table is going to be $10,000. However they gure that in 4 years their current air hockey table will be worth $500. In order to provide funds for the new table the company sets up a fund into which it places $R at the end of each month. If the fund has an interest rate of 3% compounded monthly then how much is each payment? 18. Find all solutions (using matrix reduction) of 3x + 2y + 3z = 2 2x 3y + 5z = 25 x + 5y + z = 8 19. Tom knows that he will recieve $10,000 in 4 years and $7,000 in 7 years. But unfortunately in 10 years he has to pay o a debt of $30,000. If he wants to put the money he recieved toward paying o the debt and make two equal payments in 1 year and 9 years to pay o the remainder of the debt how much must each payment be if an interest rate of 4.2% compounded daily is assumed? 20. Maximize and minimize Z = 3x 6y on the region bounded by 8 > > > > < 3y 4x 12 y + 2x 8 4y + 3x 24 > > x0 > > : y0 21. Bobby decides to put $6000 in a savings account that is compounded 23 times per year at a rate of 7.2%. Find the eective rate of interest that Bobby is earning and nd how long it will take him to have a balance of $9,000. 22. Janice has maxed out her credit card with a limit of $10,000. If the credit card company is charging her interest of 20% compounded monthly and she wants to pay o the card in 4 years with payments at the end of the month how much is each payment? If she makes her payments at the begining of the month instead how much less will the nance charge be? 23. Find all solutions that satisfy all of the following inequalities. 8 < : 7x 4y 28 5y 3x 15 9x 7y 0 24. Find two square matrices of order 2 M; N such that (MN ) = 1 10 01 Hint((MN ) 1 = N 1 M 1 ) 1