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Solve a system of 3 linear equations(3 unknowns) using inverse coefficient matrix

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Question: Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return.
You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest twice as much in B bonds as in A bonds. Let x, y, and z represent the amounts invested in AAA, A, and B bonds, respectively.
 

x
 + 
y
 + 
z
 = 
(total investment)
0.045x

 + 

0.05y

 + 

0.09z

 = 
(annual return)
2y

 − 
z
 = 
0

Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return. (Round your answers to the nearest cent.)
Total Investment      Annual Return

$12,000
    $815
amount invested in AAA-bonds     

amount invested in A-bonds 

amount invested in B-bonds 

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Answered By:

Doug C.
Math Tutor with Reputation to make difficult concepts understandable
More information: https://www.wyzant.com/Tutors/AZ/Mesa/8143904/?utm_source=youtube&utm_medium=organic&utm_campaign=aae_video

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Written Explanation:

Desmos matrix calculator:desmos.com/matrix Gaussian elimination calculator:onlinemschool.com/math/assistance/equation/gaus/
See full answer: https://www.wyzant.com/resources/answers/909360/use-the-inverse-of-the-coefficient-matrix-of-this-system-to-find-the-amount#answer-?utm_source=youtube&utm_medium=organic&utm_campaign=aae_video

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