Explanation Let x , y , z be the money borrowed by the corporation at 3%, 4%, and 5% respectively. Consider the statement “the corporation borrowed $500, 000 to expand its software line” we represent this as a linear equation as represented by, x + y + z = 500 , 000 → ( 1 ) Consider the statement “money borrowed at each rate (3%, 4%, and 5%) when the annual interest was $20, 500” we can represent this as a linear equation, as represented by, 3 100 x + 4 100 y + 5 100 z = 20 , 500 0.03 x + 0.04 y + 0.05 z = 20 , 500 → ( 2 ) Consider the statement “the amount borrowed at 4% was 2.5 times the amount borrowed at 3%.” We can represent this as a linear equation, as represented by, 2.5 x = y 2.5 x − y = 0 → ( 3 ) We represent the system of linear equations ( 1 ) , ( 2 ) and ( 3 ) as augmented matrix represented by, [ 1 0.03 2.5 1 0.04 − 1 1 0.05 0 500000 20500 0 ] Consider the augmented matrix [ 1 0.03 2.5 1 0.04 − 1 1 0.05 0 500000 20500 0 ] R 2 → R 2 − 0.03 R 1 [ 1 0.03 2.5 1 0.04 − 1 1 0.05 0 500000 20500 0 ] = [ 1 0.03 − 0.03 ( 1 ) 2.5 1 0.04 − 0.03 ( 1 ) − 1 1 0.05 − 0.03 ( 1 ) 0 500000 20500 − 0.03 ( 500000 ) 0 ] = [ 1 0 2.5 1 0.01 − 1 1 0.02 0 5000000 5500 0 ] R 3 → R 3 − 2.5 R 1 [ 1 0 2.5 1 0.01 − 1 1 0.02 0 500000 5500 0 ] = [ 1 0 2.5 − 2.5 ( 1 ) 1 0.01 − 1 − 2.5 ( 1 ) 1 0.02 0 − 2.5 ( 1 ) 500000 5500 0 − 2.5 ( 500000 ) ] = [ 1 0 0 1 0.01 − 3.5 1 0.02 − 2.5 500000 5500 − 1250000 ] R 2 → 100 R 2 [ 1 0 0 1 0.01 − 3.5 1 0.02 − 2.5 500000 5500 − 1250000 ] = [ 1 0 × 100 0 1 0

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN: 9781305658004

Author: Ron Larson

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 1.2, Problem 47E

To determine

To solve:

The system using matrices.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.2, Problem 46E

Chapter 1.2, Problem 48E

Students have asked these similar questions

Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient matrix is -23. - 5x + y − z = −7 2x-y-2z = 6 3x+2z-7

eric pez Xte in z= Therefore, we have (x, y, z)=(3.0000, 83.6.1 Exercise Gauss-Seidel iteration with Start with (x, y, z) = (0, 0, 0). Use the convergent Jacobi i Tol=10 to solve the following systems: 1. 5x-y+z = 10 2x-8y-z=11 -x+y+4z=3 iteration (x Assi 2 Assi 3. 4. x-5y-z=-8 4x-y- z=13 2x - y-6z=-2 4x y + z = 7 4x-8y + z = -21 -2x+ y +5z = 15 4x + y - z=13 2x - y-6z=-2 x-5y- z=-8 realme Shot on realme C30 2025.01.31 22:35 f

Use Pascal's triangle to expand the binomial (6m+2)^2

Chapter 1 Solutions

Elementary Linear Algebra (MindTap Course List)

Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The system using matrices.

Solution Summary: The author illustrates the system using matrices. The corporation borrowed 500, 000 to expand its software line.

Videos

To solve: The system using matrices.

Want to see the full answer?

Chapter 1 Solutions

To solve:

The system using matrices.