2) x + y + z = -1. A) Dependent B) Independent C) Inconsistent

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Willis Lee
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1 Assignment.1-. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent dependent or inconsistent. 1) x + y + z = 1) x - y + z = 5 x + y + z = 15 Dependent Independent Inconsistent Solve the system of equations. If the system is dependent express solutions in terms of the parameter z. ) x + y + z = ) x - y + z = -8 x + y + z = (-5 1 ) No solution ( 1-5) (-5 1) Solve the system of two equations in two variables. ) x + y = ) 0x + 0y = 10 No solution - y + 1 y for any real number y Determine whether the given ordered set of numbers is a solution of the system of equations. ) (- ) ) x + y = -8 x + y = -8 Yes No Solve the system of equations. If the system is dependent express solutions in terms of the parameter z. 5) x + y + 7z = -5 -x - y + 7z = 5 5) z z z -0-8z 80-0z z z -5 - x - 7z z z -5 + x + 7z z Perform the row operations on the matrix and write the resulting matrix. ) Replace R by R1 + ()R )

2 7) Replace R by 1 R R 7) Determine whether the given ordered set of numbers is a solution of the system of equations. 8) ( 1) 8) x + y = 7 x + y = Yes No Solve the system of two equations in two variables. 9) 5x - y = 8 9) 5x - 10y = No solution (0 -) (1 0) (1.5) Solve the problem by writing and solving a suitable system of equations. 10) Alan invests a total of $10500 in three different ways. He invests one part in a mutual fund which 10) in the first year has a return of %. He invests the second part in a government bond at 7% per year. The third part he puts in the bank at 5% per year. He invests twice as much in the mutual fund as in the bank. The first year Alan's investments bring a total return of $85. How much did he invest in each way? mutual fund: $000; bond: $7000: bank: $1500 mutual fund: $000; bond: $000: bank: $1500 mutual fund: $00; bond: $5100: bank: $1800 mutual fund: $00; bond: $900: bank: $100 ) Mike Joe and Bill are painting a fence. The painting can be finished if Mike and Joe work together ) for hours and Bill works alone for hours or if Mike and Joe work together for hours and Bill works alone for 5 hours or if Mike works alone for hours Joe works alone for hours and Bill works alone for 1 hour. How much time does it take for each man working alone to complete the painting? Mike 8 hr Joe 8 hr Bill 1 hr Mike 1 hr Joe 10 hr Bill 10 hr Mike 8 hr Joe 1 hr Bill 8 hr Mike 1 hr Joe 8 hr Bill 8 hr Use the Gauss-Jordan method to solve the system of equations. 1) x - y + z = -8 1) x + y + z = - x + y - z = 0 No solution (- - ) (- - ) (- -)

3 1) x + y - z = 7 1) x - 8y - 9z = -9 x + y + z = 9 (- ) ( 9 ) No solution ( 9) 1) x - y + z = -8 1) x + 5y + z = 0 5x + y + 1z = 10 (0 8 0) (8 8 0) No solution (8 0 8) 15) Factories A and B sent rice to stores 1 and. A sent 10 loads and B sent. Store 1 used 15 loads and 15) store used 17. It cost $00 to ship from A to 1 $50 from A to $00 from B to 1 and $50 from B to. $7750 was spent. How many loads went where? 9 from A to 1 1 from A to from B to 1 from Y to B 8 from A to 1 from A to 7 from B to 1 15 from B to 0 from A to 1 10 from A to 17 from B to 1 5 from B to 10 from A to 1 0 from A to 5 from B to 1 17 from B to Use the Gauss-Jordan method to solve the system of equations. 1) 5x - y + z = 8 7x + y + z = 1) 1x + z = 1 -z + 7 z - 7 z + 1 -z - 1 z z z + 7 -z + 7 -z - 1 z - 1 z z 17) x - y + z = 1 17) x + z = x + y + z = - No solution (0 - ) ( 0 -) ( - 0) 18) x + 8y + 8z = 8 18) 7x + 7y + z = 1 8x + 15y + 9z = -9 (0 0 1) ( 0 1) No solution (1 1) 19) x + y + z = 5 19) x + 5y - z = -8 10x + 7y + z = z + -z + 7z - -7z - z z -z + z + 7z - 7z + z z

4 0) Linda invests $5000 for one year. Part is invested at 5% another part at % and the rest at 8%. 0) The total income from all investments is $100. The income from the 5% amd % investments is the same as the income from the 8% investment. Find the amount invested at each rate. $10000 at 5% $10000 at % $5000 at 8% $10000 at 5% $5000 at % $10000 at 8% $8000 at 5% $10000 at % $7000 at 8% $5000 at 5% $10000 at % $10000 at 8% Perform the indicated operation where possible. 1) ) ) What is the size of the matrix? ) x x Perform the indicated operation. ) Let A = and B = 0. Find A + B. ) Write a matrix to display the information. ) Factory A makes 1 model-a 5 model-d and 5 model-m train sets. Factory B makes 5 model-a ) 8 model-d and 8 model-m train sets. If model-a sells for $19 model-d for $ and model-m for $ write a x matrix to summarize the income by model Perform the indicated operation. 5) Let C = -. Find C. 5) 8-8

5 ) Carney and Dobler sell home and mortgage insurance. Their sales for the months of May and June ) are given in the matrices. M = Home Mortgage Carney Dobler J = Carney Dobler Find the matrix that would give the change in sales from May to June Perform the indicated operation where possible. 7) ) Perform the indicated operation. 1 8) Let C = - and D = Find C - D. 8) ) The matrix shows the average number of wax and buff treatments each of workers in a car wash 9) can do in a day. Give the matrix that shows what each worker can do in days. T = Wax Buffs Ford Morton Porter

6 Perform the indicated operation where possible. 0) 0-0)

Week 1 (8/24/2004-8/30/2004) Read 2.1: Solution of linear system by the Echelon method

Week 1 (8/24/2004-8/30/2004) Read 2.1: Solution of linear system by the Echelon method Important Terms and Concepts: Possibilities for the solutions of a system of two linear equations in two unknowns