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 $z$: