Explanation Given: The constraint of the system is as follows, { x + y + z = ( total investment ) 0.045 x + 0.05 y + 0.09 z = ( annual return ) 2 y − z = 0 The total amount invested is $ 12 , 000 . The annual return is $ 835 . Approach: If A is an invertible matrix, then the system of linear equations represented by A X = B has a unique solution given by X = A − 1 B . Calculation: Let the amount invested in AAA bond be x , in A be y, and in B be z . The system of linear constraint is, x + y + z = 12 , 000 0.045 x + 0.05 y + 0.09 z = 835 2 y − z = 0 Write the system of equation in the form A X = B . [ 1 1 1 0.045 0.05 0.09 0 2 − 1 ] [ x y z ] = [ 12000 835 0 ] ... ( 1 ) Substitute A for [ 1 1 1 0.045 0.05 0.09 0 2 − 1 ] in equation ( 1 ) . A [ x y z ] = [ 12000 835 0 ] [ x y z ] = A − 1 [ 12000 835 0 ] ... ( 2 ) Calculate A − 1 Proceed by adjoining the identity matrix to form the matrix, [ A ⋮ I ] = [ 1 1 1 ⋮ 1 0 0 0.045 0.05 0.09 ⋮ 0 1 0 0 2 − 1 ⋮ 0 0 1 ] Use the elementary row operation to obtain the form of [ I ⋮ A − 1 ] . Apply operation R 2 → R 2 − 9 200 R 1 . [ A ⋮ I ] = [ 1 1 1 ⋮ 1 0 0 0 1 / 200 9 / 200 ⋮ − 9 / 200 1 0 0 2 − 1 ⋮ 0 0 1 ] Apply operation R 1 → R 1 − 200 R 2 and R 3 → R 3 − 400 R 2 . [ A ⋮ I ] = [ 1 0 − 8 ⋮ 10 − 200 0 0 1 / 200 9 / 200 ⋮ − 9 / 200 1 0 0 0 − 19 ⋮ 18 − 400 1 ] Apply operation R 2 → 200 R 2 [ A ⋮ I ] = [ 1 0 − 8 ⋮ 10 − 200 0 0 1 9 ⋮ − 9 200 0 0 0 − 19 ⋮ 18 − 400 1 ] Apply operation R 3 → − 1 19 R 3

10th Edition

ISBN: 9781337683074

Author: Larson

Publisher: CENGAGE L

See similar textbooks

Videos

Question

Chapter 8.3, Problem 58E

To determine

To find:

The amount invested in each type of bond using inverse matrix if total amount invested is $12,000.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 57E

Chapter 8.3, Problem 59E

Students have asked these similar questions

Explain the key points of 11.5.2

Explain the key points of 11.3.5

Practice using 11.5.2 to derive 11.6.1

Chapter 8 Solutions

PRECALCULUS-WEBASSIGN EPIN K12 ACCESS

Ch. 8.1 - Prob. 1CP Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 1E

Knowledge Booster

$Calculus$

Learn more about

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

The amount invested in each type of bond using inverse matrix if total amount invested is $ 12 , 000 .

Solution Summary: The author analyzes the system of linear equations represented by AX=B with a unique solution.

Videos

To find:

The amount invested in each type of bond using inverse matrix if total amount invested is $12,000.

Want to see the full answer?

Chapter 8 Solutions

The amount invested in each type of bond using inverse matrix if total amount invested is $ 12 , 000 .

Solution Summary: The author analyzes the system of linear equations represented by AX=B with a unique solution.

Videos

To find: The amount invested in each type of bond using inverse matrix if total amount invested is $12,000.

Want to see the full answer?

Chapter 8 Solutions

To find:

The amount invested in each type of bond using inverse matrix if total amount invested is $12,000.