investments. Part of the money is invested in a savings account with an annual rate of interest of 6%, part in. 7% annual yield bonds, and the remainder in a business. In 2006, when he lost 6% of the money that he invested in that business, his net income from all three investments was 660. If he invested 3000 more in the business than in the savings account, how much was through matrix method 

Let's set up the problem and solve it using a system of linear equations and then apply the matrix method to find the solution.

### Step 1: Define the Variables
Let:
- $ x $ = amount invested in the savings account (6% interest)
- $ y $ = amount invested in the bonds (7% interest)
- $ z $ = amount invested in the business (lost 6% in 2006)

### Step 2: Translate the Problem into Equations
1. **Interest Income Equation**: The total income from all three investments in 2006 was $660. Thus,
   \[
   0.06x + 0.07y - 0.06z = 660
   \]

2. **Business Investment Relation**: The amount invested in the business was $3000 more than in the savings account, so:
   \[
   z = x + 3000
   \]

3. **Total Investment Relation**: We need another equation involving $ x $, $ y $, and $ z $ to solve for the exact amounts. Since no total investment amount is given, we assume a system where these two main relationships are solved independently, as the third relation isn't provided.

### Step 3: Substitute and Set Up Equations in Matrix Form
Using $ z = x + 3000 $ in the first equation, we get:
\[
0.06x + 0.07y - 0.06(x + 3000) = 660
\]
Simplify this equation:
\[
0.06x + 0.07y - 0.06x - 180 = 660
\]
\[
0.07y = 840
\]
So:
\[
y = \frac{840}{0.07} = 12000
\]

Now, substitute $ y = 12000 $ back to find $ x $ and $ z $:


Investments. Part of the money is invested in a savings account with an annual rate of interest of 6%, part in 7% annual yield bonds, and the remainder in a business. In 2006, when he lost 6% of the money that he invested in that business, his net income from all three investments was 660. If he invested 3000 more in the business than in the savings account, how much was invested through matrix method?

Learn how to determine the investment allocation in a savings account, bonds, and a business using matrix methods. This problem includes calculating net income with interest and loss, using linear equations and matrix solutions. Ideal for students in Grades 11-12.

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