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November 7th, 2017, 07:46 AM   #1
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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.
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November 7th, 2017, 11:06 AM   #2
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Quote:
Originally Posted by PJH111 View Post
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.
...
$2x$ = amount invested in AAA bonds

$y$ = 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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