Mathematics 10 — Exercise 3.3 · Q3 (iii)

Full question

Find the additive inverse of the following matrix.

Step-by-step solution

1. Multiply every matrix entry by the scalar.

   $$(-1,\left[\begin{array}{cc}2& -1\\ -2& 3\end{array}\right])$$

2. Entry (1,1): multiply its value by the scalar.

   $$\left(-1\right)\times 2=-2$$

3. Entry (1,2): multiply its value by the scalar.

   $$\left(-1\right)\times \left(-1\right)=1$$

4. Entry (2,1): multiply its value by the scalar.

   $$\left(-1\right)\times \left(-2\right)=2$$

5. Entry (2,2): multiply its value by the scalar.

   $$\left(-1\right)\times 3=-3$$

6. Place the calculated entries in their original row and column positions.

   $$\left[\begin{array}{cc}-2& 1\\ 2& -3\end{array}\right]$$

Answer

The final answer is shown below.