Question 1099126
<br>I assume you are to solve this using Gauss-Jordan elimination....<br>
There's no two ways about it: with the number of steps it takes to complete a Gauss-Jordan elimination, it is exasperatingly easy to make silly arithmetic errors.  I know the process very well; but in doing ten of these I will get to the right answer on the first try on only 4 or 5 of them.<br>
It would be good if there were a way for you and me to carry on a conversation about this problem.  However, I don't know how to do that on this web site, or if it is even possible.  So I will go through the details of a solution; then I hope that, if this is for an assignment to be turned in and graded, you will look at it and understand it -- instead of just turning it in and thus learning nothing from it.<br><br>
Let a =  amount invested in money markets
b = amount in bonds
c = amount in international stocks
d = amount in domestic stocks<br>
Then...
(1) {{{a+b+c+d = 220000}}}   [the total amount invested is $220,000]
(2) {{{a+b = 132000}}}   [the total invested in money markets and bonds is 60% of the total]
(3) {{{d = 4c}}}   [the amount invested in domestic stocks is 4 times the amount invested in international stocks]]
(4) {{{.025a+.035b+.04c+.06d = 8800}}}   [the desired annual return is $8,800]<br>
For solving with matrices, we need to write equation (3) as {{{4c-d=0}}}.  And those decimals in equation (4) would cause a lot of difficulty; multiplying equation (4) by 200 will get rid of the decimals, giving
{{{5a+7b+8c+12d=1760000}}}<br>
So our beginning matrix is<br>
{{{matrix(4,5,1,1,1,1,220000,1,1,0,0,132000,0,0,4,-1,0,5,7,8,12,1760000)}}}<br>
Our first objective is to get "1,0,0,0" in column 1.  We use the 1 in position (1,1) to get 0's in the rest of column 1.
>>replace row 2 with (row 1 minus row 2)
>>replace row 4 with (row 4 minus 5 times row 1)
{{{matrix(4,5,1,1,1,1,220000,0,0,1,1,88000,0,0,4,-1,0,0,2,3,7,660000)}}}<br>
Our next objective is to get a 1 in position (2,2).  But outside of row 1, the only non-zero number in column 2 is in row 4.  So let's move row 4 up to row 2, and move rows 2 and 3 down.  And while we're doing that, let's divide the new row 2 by 2 so that we have the required 1 in position (2,2).
{{{matrix(4,5,1,1,1,1,220000,0,1,1.5,3.5,330000,0,0,1,1,88000,0,0,4,-1,0)}}}<br>
Next use the 1 in position (2,2) to get a 0 in position (1,2), completing column 2.
>>replace row 1 with (row 1 minus row 2)
{{{matrix(4,5,1,0,-.5,-2.5,-110000,0,1,1.5,3.5,330000,0,0,1,1,88000,0,0,4,-1,0)}}}<br>
Next we want to get "0,0,1,0" in column 3.  We already have the required 1 in position (3,3); use it to get 0's in the other rows of column 3.
>>replace row 1 with (row 1 plus .5 times row 3)
>>replace row 2 with (row 2 minus 1.5 times row 3)
>>replace row 4 with (row 4 minus 4 times row 3)
{{{matrix(4,5,1,0,0,-2,-66000,0,1,0,2,198000,0,0,1,1,88000,0,0,0,-5,-352000)}}}<br>
Next divide row 4 by -5 to get the required 1 in position (4,4).
{{{matrix(4,5,1,0,0,-2,-66000,0,1,0,2,198000,0,0,1,1,88000,0,0,0,1,70400)}}}<br>
And finally use row 4 to get 0's in the other rows of column 4.
>>replace row 1 with (row 1 plus 2 times row 4)
>>replace row 2 with (row 2 minus 2 times row 4)
>>replace row 3 with (row 3 minus row 4)
{{{matrix(4,5,1,0,0,0,74800,0,1,0,0,57200,0,0,1,0,17600,0,0,0,1,70400)}}}<br><br>
We have our answer.<br>
She needs to invest $74,800 in money markets, $57,200 in bonds, $17,600 in international stocks, and $70,400 in domestic stocks.