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November 7th, 2017, 07:46 AM  #1 
Newbie Joined: Nov 2017 From: MD Posts: 1 Thanks: 0  Help with Matrix Problem
Here is the question Bond Investment: An investment company recommends that a client invest in AAA, AA, and A rated bonds. The average annual yield on AAA bonds is 6%, on AA bonds 7%, and on A bonds 10%. The client tells the company she wants to invest twice as much in AAA bonds as in A bonds. How much should be invested in each if the total investment is $50,000 and the investor wants an annual income that is, earned interest, of $3,620. You have to use the inverse matrix to find your solution. Show your steps to get full credit. I use this as first matrix 1, 1, 1, 1, 0, 0 ,1 as first row 0.1, 0.07, 0.06, 0, 1, 0 as second row 2, 0, 1, 0, 0, 1 as third row Is that correct? Then after doing Gauss method to find inverse my answer is as follows: 7 100 1 22 300 4 14 200 3 Just need verification if I did it right. Thanks Last edited by PJH111; November 7th, 2017 at 07:56 AM. 
November 7th, 2017, 11:06 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,662 Thanks: 1327  Quote:
$y$ = amount invested in AA bonds $x$ = amount invested in A bonds $3x+y = 50000$ $2x(0.06) + y(0.07) + x(0.10) = 3620$ $\begin{bmatrix} 3 & 1\\ .22 & .07 \end{bmatrix} \cdot \begin{bmatrix} x\\ y \end{bmatrix}= \begin{bmatrix} 50000\\ 3620 \end{bmatrix}$  

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