A trust fund has Rs. 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of (i) Rs 1800 (ii) 2000.

Explanation

To solve the problem of how to invest Rs. 30,000 in two different types of bonds to achieve a specific annual interest, we can set up a system of equations and use matrix multiplication. Let's break down the solution step by step.

### Step 1: Define Variables
Let:
- \( x \) = amount invested in the first bond (5% interest)
- \( 30000 - x \) = amount invested in the second bond (7% interest)

### Step 2: Set Up the Interest Equation
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