Homework Help is Here – Start Your Trial Now!
Math
Calculus
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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 15E
See similar textbooks
icon
Related questions
Question
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
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9780998625720
Author:
Lynn Marecek
Publisher:
OpenStax College
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS