Let these investments be ₹x, ₹y and ₹z, respectively.
Then, x + y + z = 5000
6x/100 + 7y/100 + 8z/100 = 358
6x + 7y + 8z = 35800
And, 6x/100 + 7y/100 = 8z/100 + 70
6x + 7y - 8z = 7000.
Representing in the matrix form,
AX = B
\(\begin{bmatrix}1&1&1\\0&1&2\\0&0&-16\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}5000\\5800\\-28800\end{bmatrix}\)
\(R_3\rightarrow\frac{R_3}{-16}\)
\(\begin{bmatrix}1&1&1\\0&1&2\\0&0&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}5000\\5800\\1800\end{bmatrix}\)
\(R_1\rightarrow R_1-R_2\)
\(\begin{bmatrix}1&0&-1\\0&1&2\\0&0&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}-800\\5800\\1800\end{bmatrix}\)
\(R_1\rightarrow R_1+R_3\)
\(R_2\rightarrow R_2-2R_3\)
\(\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1000\\2200\\1800\end{bmatrix}\)
\(\Rightarrow\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1000\\2200\\1800\end{bmatrix}\)
\(\Rightarrow\) x = 1000,
y = 2200
and z = 1800.