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Taika invested a total of $ (a+b+c+ 900) × 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, y be the amount invested in the 4% account, and z be the amount invested in the 5% account. (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. 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. NISS

Taika invested a total of $ (a+b+c+ 900) × 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, y be the amount invested in the 4% account, and z be the amount invested in the 5% account. (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. 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. NISS

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 6CM
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I attached the answer of part c(3) In view of part c solve d part
11:58 bo a) 0 46 | | 2 61% 01:44 Augmented matrix of corresponding to system is 1 3 4 5 : (+720) 5000 2 0 * b Step2 b) we have to solve this system using Graussian elimination. to Convert system in row echlone. form. So, applying row operations. R3 = R₂-2R₁ R₂= R₂-3R₁ I 1 : (a+b+c+ 900) 1000 0 1 2 (2c-3a-3b+900) 1000 o -2 -3 (a+b+c+ 900) 2000 R3= R3+2R₂ T 1 1 : (a+b+c + 900) 1000 O 1 2 : (24-39-3b +900) 1000 O 1 : (C-49-46) 2000 R₂= R₂-3 1 1 : (a+b+c+900) 1000 O O : (13a +13b-2c + 900) 1000 O 1 : (c-49-4b) 2000 R₁ = R₁ - R₂-R3 O 0 (C-49-46) 1000 O 1 0 (139+13b-2C+900) 1000 0 O 1: (C-49-46) 2000 Hence the results are x= ((-49-46) 1000, y = (139+13b-2(+900) 1000, Z = (C-49-46) 2000. 8 020 I : (a+b+c+ 900) 1000 J LX Do
Transcribed Image Text:11:58 bo a) 0 46 | | 2 61% 01:44 Augmented matrix of corresponding to system is 1 3 4 5 : (+720) 5000 2 0 * b Step2 b) we have to solve this system using Graussian elimination. to Convert system in row echlone. form. So, applying row operations. R3 = R₂-2R₁ R₂= R₂-3R₁ I 1 : (a+b+c+ 900) 1000 0 1 2 (2c-3a-3b+900) 1000 o -2 -3 (a+b+c+ 900) 2000 R3= R3+2R₂ T 1 1 : (a+b+c + 900) 1000 O 1 2 : (24-39-3b +900) 1000 O 1 : (C-49-46) 2000 R₂= R₂-3 1 1 : (a+b+c+900) 1000 O O : (13a +13b-2c + 900) 1000 O 1 : (c-49-4b) 2000 R₁ = R₁ - R₂-R3 O 0 (C-49-46) 1000 O 1 0 (139+13b-2C+900) 1000 0 O 1: (C-49-46) 2000 Hence the results are x= ((-49-46) 1000, y = (139+13b-2(+900) 1000, Z = (C-49-46) 2000. 8 020 I : (a+b+c+ 900) 1000 J LX Do
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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