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(a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert this system to an augmented matrix. (c) Use a spreadsheet and Gaussian elimination with matrices to find the amount that was invested at each interest rate. Include two screenshots: (1) the formula view (or put in front to keep them from evaluating) of your spreadsheet (2) the results.

(a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert this system to an augmented matrix. (c) Use a spreadsheet and Gaussian elimination with matrices to find the amount that was invested at each interest rate. Include two screenshots: (1) the formula view (or put in front to keep them from evaluating) of your spreadsheet (2) the results.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve b and c part only in 30 min
Solution a) let x be the amount invested in the 3% account. y be the amount invested in the 4% Account and z be the amount invested in the 5%. account. According to the question, x+y+z = (a+b+c+900) x 1000 => ·x+y+z = 1000 a +1000 b + 1000 € + 900000 Also, Total annual interest on the three investment was $(C+720) x 50 xx3x1 gx4xi = 500 +720x50 +2x5x1 100 100 100 → 3x + (2) +4y+52 = +52 = 5000c + 3600000 Also, Twice as much is invested at 3% money invested at 5% 2x = Z 2x - 2 = 0 linear .. The required system of x+y+z 2 = 1000 a +10006 +1000c + 900000 3x + 4y + 5z = 5000 C +3600000 2x -N + as equations for x, y, z ore
Transcribed Image Text:Solution a) let x be the amount invested in the 3% account. y be the amount invested in the 4% Account and z be the amount invested in the 5%. account. According to the question, x+y+z = (a+b+c+900) x 1000 => ·x+y+z = 1000 a +1000 b + 1000 € + 900000 Also, Total annual interest on the three investment was $(C+720) x 50 xx3x1 gx4xi = 500 +720x50 +2x5x1 100 100 100 → 3x + (2) +4y+52 = +52 = 5000c + 3600000 Also, Twice as much is invested at 3% money invested at 5% 2x = Z 2x - 2 = 0 linear .. The required system of x+y+z 2 = 1000 a +10006 +1000c + 900000 3x + 4y + 5z = 5000 C +3600000 2x -N + as equations for x, y, z ore
2. Taika invested a total of $ (a + b + c + 900) x 1,000 into three investment accounts, paying 3%,4%, and 5% simple interest per year. The annual interest earned on the three investments was $ (c + 720) x 50. Twice as much money is invested at 3% as invested at 5%. Let x be the amount invested in the 3% account, and z be the amount invested in the 5% account. y be the amount invested in the 4% account, O 0 (a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert this system to an augmented matrix. (c) Use a spreadsheet and Gaussian elimination with matrices to find the amount that was invested at each interest rate. Include two screenshots: SS (1) the formula view (or put in front to keep them from evaluating) of your spreadsheet (2) the results. Note: (Using methods other than Gaussian Elimination will result in heavy mark losses. You need to convert your matrix into row-echelon form.) (d) Check your answer for part (c) by substituting your solutions into the system of equations. N
Transcribed Image Text:2. Taika invested a total of $ (a + b + c + 900) x 1,000 into three investment accounts, paying 3%,4%, and 5% simple interest per year. The annual interest earned on the three investments was $ (c + 720) x 50. Twice as much money is invested at 3% as invested at 5%. Let x be the amount invested in the 3% account, and z be the amount invested in the 5% account. y be the amount invested in the 4% account, O 0 (a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert this system to an augmented matrix. (c) Use a spreadsheet and Gaussian elimination with matrices to find the amount that was invested at each interest rate. Include two screenshots: SS (1) the formula view (or put in front to keep them from evaluating) of your spreadsheet (2) the results. Note: (Using methods other than Gaussian Elimination will result in heavy mark losses. You need to convert your matrix into row-echelon form.) (d) Check your answer for part (c) by substituting your solutions into the system of equations. N
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