Solution:
Suppose the investments are 
Therefore, 
And, 
Now converting in the matrix form,
![\begin{array}{l} A X=B \\ {\left[\begin{array}{ccc} 1 & 1 & 1 \\ 6 & 7 & 8 \\ 6 & 7 & -8 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 5000 \\ 35800 \\ 7000 \end{array}\right]} \\ R_{3}-R_{2} \\ {\left[\begin{array}{ccc} 1 & 1 & 1 \\ 6 & 7 & 8 \\ 0 & 0 & -16 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 5000 \\ 35800 \\ -28800 \end{array}\right]} \\ R_{2}-6 R_{1} \\ {\left[\begin{array}{ccc} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & -16 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 5000 \\ 5800 \\ -28800 \end{array}\right]} \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-38e2270edc83da2ddede5ae897a9f99c_l3.png "Rendered by QuickLaTeX.com")
Again converting into the equations we get
Amount of 
An amount of ₹ 5000 is put into three investments at 6%, 7% and 8% per annum respectively. The total annual income from these investments is ₹358. If the total annual income from first two investments is ₹70 more than the income from the third, find the amount of each investment by the matrix method. HINT: Let these investments be ₹x, ₹y and ₹z, respectively. Then, 
