Anish Buchanan

2020-11-27

Using Matrices, solve the following: A practical Humber student invested 20,000 in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was \$1,880. How much does the student invested in each stock?

Step 1
Let x be the amount invested at 7%
y be the amount invested at 11%
Total amount invested = 20000
Thus, x+y=20000 ...(1)
Thus, 0.07x+0.11y=1880 ...(2)
step 2
Hence we have two system of equations
x+y=20000
0.07x+0.11y=1880
we solve it by matrices
It can be expressed as
$\left[\begin{array}{cc}1& 1\\ 0.07& 0.11\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}20000\\ 1880\end{array}\right]$
Augmented Matrix for Ax=b is
$\left[\begin{array}{ccc}1& 1& 20000\\ 0.07& 0.11& 1880\end{array}\right]$
${R}_{2}\to {R}_{2}-0.07{R}_{1}\left[\begin{array}{ccc}1& 1& 20000\\ 0.07& 0.11& 1880\end{array}\right]$
Which can be expressed as
x+y=20000
0.04y=480
$⇒y=12000$ And, $x=20000-12000=8000$ Hence $\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}8000\\ 12000\end{array}\right]$
Step 3
ANSWER:The student invested 8,000 at 7% interest and 12,000 at 11% interest

Jeffrey Jordon